Edit Profile (opens in new tab) Simos, Theodore E. Compute Distance To: Compute Author ID: simos.theodore-e Published as: Simos, T. E.; Simos, Theodore E.; Simos, Theodore more...less Homepage: http://theodoresimos.org/ External Links: MGP · Google Scholar · ResearchGate · dblp · GND Documents Indexed: 429 Publications since 1987, including 1 Book 43 Contributions as Editor Reviewing Activity: 63 Reviews Co-Authors: 113 Co-Authors with 364 Joint Publications 1,471 Co-Co-Authors all top 5 Co-Authors 94 single-authored 55 Tsitouras, Charalampos 39 Kalogiratou, Zacharoula 32 Alolyan, Ibraheem 32 Anastassi, Zacharias A. 21 Medvedev, Maxim A. 16 Monovasilis, Theodoros 16 Psihoyios, George 15 Lin, Chialiang 15 Medvedeva, Marina A. 15 Vlachos, D. S. 13 Avdelas, George 12 Vigo-Aguiar, Jesus 11 Liu, Chenglian 9 Konguetsof, Avrilia 9 Maroulis, George 9 Raptis, A. D. 9 Williams, P. S. 8 Kovalnogov, Vladislav N. 7 Panopoulos, G. A. 7 Sakas, D. P. 6 Famelis, Ioannis Th. 6 Fedorov, Ruslan V. 6 Hsu, Chieh-Wen 5 Berg, Dmitry B. 5 Papakaliatakis, G. 5 Tselios, Kostas 4 Monovasilis, Theodore 4 Papadopoulos, D. F. 4 Papageorgiou, George 3 Fang, Jie 3 Hui, Fei 3 Kalvouridis, Tilemahos J. 3 Katsikis, Vasilios N. 3 Kosti, Athinoula A. 3 Mitsou, G. V. 3 Ramos, Higinio 3 Sideridis, A. B. 3 Wang, Zenggui 2 Bondarenko, Aleksandr Adamovich 2 Cash, Jeff R. 2 Chen, Zhong 2 Ferrándiz, José Manuel 2 Luo, Jun 2 Ma, Yu-Yu 2 Mourtas, Spyridon D. 2 Ning, Hang 2 Papageorgiou, C. D. 2 Shi, Xin 2 Stavroyiannis, S. 2 Varagouli, E. G. 2 Xeidakis, G. S. 2 Xi, Xiaopeng 2 Yan, Ke 2 Yao, Junfeng 2 Zeidan, Dia 2 Zhao, Zhen 2 Zhou, Zhou 1 Aguiar, J. V. 1 Allison, A. C. 1 Anatassi, Zacharias 1 Batzias, Fragiskos 1 Chen, Jwu Jenq 1 Chen, Xiaoping 1 Chenga, Xin 1 De, Ashoke 1 Dimas, E. E. 1 Dong, Ming 1 Generalov, Dmitry 1 Golovanov, Viktor M. 1 Goncalves, Eric 1 Gürlebeck, Klaus 1 Hao, Ruru 1 Hao, Sheng 1 Harley, Charis 1 Hou, Chih-Chun 1 Huang, Junjie 1 Kefalidis, E. 1 Kosinski, Pawel 1 Kosmas, Odysseas 1 Kostishko, Boris M. 1 Lei, Tao 1 Li, Xingyuan 1 Liang, Minjian 1 Lv, Jieyin 1 Ma, Jing 1 Ma, Junyan 1 Manousopoulos, P. D. 1 Mingliang, Zheng 1 Mu, Kenan 1 Mylonas, A. B. 1 Psihoyios, Georgios 1 Qiu, Guohua 1 Qiu, Junlai 1 Stasinos, P. I. 1 Stefanis, B. 1 Sun, Bin 1 Suranov, D. V. 1 Thomakos, Dimitrios D. 1 Tong, Xing 1 Tougelidis, G. ...and 13 more Co-Authors all top 5 Serials 154 Journal of Mathematical Chemistry 31 Journal of Computational and Applied Mathematics 27 Mathematical Methods in the Applied Sciences 24 Computer Physics Communications 20 MATCH - Communications in Mathematical and in Computer Chemistry 17 Computers & Mathematics with Applications 17 AIP Conference Proceedings 15 Applied Mathematics and Computation 14 International Journal of Modern Physics C 9 Mathematical and Computer Modelling 7 Computers and Chemistry 7 Lecture Series on Computer and Computational Sciences 6 Journal of Computational Physics 6 Applied Mathematics Letters 6 ANACM. Applied Numerical Analysis and Computational Mathematics 6 Mediterranean Journal of Mathematics 5 Applied and Computational Mathematics 4 Physics Letters. A 4 Molecular Simulation 4 Numerical Algorithms 3 International Journal of Modern Physics A 3 Astrophysics and Space Science 3 Applied Numerical Mathematics 2 Helvetica Physica Acta 2 IMA Journal of Numerical Analysis 2 Computing 2 Japan Journal of Industrial and Applied Mathematics 2 Applied Mathematical Modelling 2 International Journal of Computer Mathematics 2 Abstract and Applied Analysis 2 Journal of Statistics & Management Systems 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Journal of Computational Methods in Sciences and Engineering 1 Modern Physics Letters A 1 Computers and Structures 1 International Journal of Theoretical Physics 1 Physics Reports 1 ACM Transactions on Mathematical Software 1 BIT 1 Match 1 Mathematics and Computers in Simulation 1 Acta Applicandae Mathematicae 1 Journal of Computational Mathematics 1 Computational Mechanics 1 Journal of Scientific Computing 1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 1 Celestial Mechanics 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 Filomat 1 Parallel Algorithms and Applications 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Journal of Applied Mathematics 1 Advances in Mathematical Physics all top 5 Fields 424 Numerical analysis (65-XX) 188 Ordinary differential equations (34-XX) 117 Quantum theory (81-XX) 42 General and overarching topics; collections (00-XX) 27 Dynamical systems and ergodic theory (37-XX) 27 Mechanics of particles and systems (70-XX) 17 Biology and other natural sciences (92-XX) 14 Partial differential equations (35-XX) 13 Fluid mechanics (76-XX) 12 Computer science (68-XX) 8 Mechanics of deformable solids (74-XX) 7 Statistics (62-XX) 7 Classical thermodynamics, heat transfer (80-XX) 7 Operations research, mathematical programming (90-XX) 6 Optics, electromagnetic theory (78-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 2 Number theory (11-XX) 2 Operator theory (47-XX) 2 Information and communication theory, circuits (94-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Special functions (33-XX) 1 Functional analysis (46-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 370 Publications have been cited 10,990 times in 729 Documents Cited by ▼ Year ▼ A finite-difference method for the numerical solution of the Schrödinger equation. Zbl 0877.65054Simos, T. E.; Williams, P. S. 153 1997 A four-step phase-fitted method for the numerical integration of second order initial-value problems. Zbl 0726.65089Raptis, A. D.; Simos, T. E. 124 1991 Exponentially and trigonometrically fitted methods for the solution of the Schrödinger equation. Zbl 1192.65111Simos, T. E. 122 2010 An optimized Runge-Kutta method for the solution of orbital problems. Zbl 1063.65059Anastassi, Z. A.; Simos, T. E. 118 2005 Closed Newton-Cotes trigonometrically-fitted formulae of high order for long-time integration of orbital problems. Zbl 1171.65449Simos, T. E. 118 2009 Optimization as a function of the phase-lag order of nonlinear explicit two-step \(P\)-stable method for linear periodic IVPs. Zbl 1169.65324Stavroyiannis, S.; Simos, T. E. 113 2009 Runge-Kutta methods with minimal dispersion and dissipation for problems arising from computational acoustics. Zbl 1063.65113Tselios, Kostas; Simos, T. E. 110 2005 A fourth algebraic order trigonometrically fitted predictor-corrector scheme for IVPs with oscillating solutions. Zbl 1063.65060Psihoyios, G.; Simos, T. E. 103 2005 Multiderivative methods of eighth algebraic order with minimal phase-lag for the numerical solution of the radial Schrödinger equation. Zbl 1063.65067Sakas, D. P.; Simos, T. E. 103 2005 Newton–Cotes formulae for long-time integration. Zbl 1041.65104Kalogiratou, Z.; Simos, T. E. 103 2003 Symplectic integrators for the numerical solution of the Schrödinger equation. Zbl 1027.65171Kalogiratou, Z.; Monovasilis, Th.; Simos, T. E. 103 2003 Trigonometrically fitted predictor–corrector methods for IVPs with oscillating solutions. Zbl 1027.65095Psihoyios, G.; Simos, T. E. 103 2003 New modified Runge-Kutta-Nyström methods for the numerical integration of the Schrödinger equation. Zbl 1202.65092Kalogiratou, Z.; Monovasilis, Th.; Simos, T. E. 103 2010 High order closed Newton-Cotes trigonometrically-fitted formulae for the numerical solution of the Schrödinger equation. Zbl 1161.65091Simos, T. E. 101 2009 A generator of hybrid symmetric four-step methods for the numerical solution of the Schrödinger equation. Zbl 1027.65094Konguetsof, A.; Simos, T. E. 98 2003 A parametric symmetric linear four-step method for the efficient integration of the Schrödinger equation and related oscillatory problems. Zbl 1246.65105Anastassi, Z. A.; Simos, T. E. 98 2012 Zero dissipative, explicit Numerov-type methods for second order IVPs with oscillating solutions. Zbl 1031.65080Simos, T. E.; Famelis, I. T.; Tsitouras, C. 97 2003 Construction of an optimized explicit Runge-Kutta-Nyström method for the numerical solution of oscillatory initial value problems. Zbl 1222.65066Kosti, A. A.; Anastassi, Z. A.; Simos, T. E. 96 2011 Dissipative trigonometrically-fitted methods for linear second-order IVPs with oscillating solution. Zbl 1062.65075Simos, T. E. 95 2004 On modified Runge-Kutta trees and methods. Zbl 1231.65118Tsitouras, Ch.; Famelis, I. Th.; Simos, T. E. 95 2011 A new Numerov-type method for the numerical solution of the Schrödinger equation. Zbl 1183.81060Simos, T. E. 92 2009 An exponentially-fitted Runge-Kutta method for the numerical integration of initial-value problems with periodic or oscillating solutions. Zbl 1001.65080Simos, T. E. 91 1998 Construction of exponentially fitted symplectic Runge-Kutta-Nyström methods from partitioned Runge-Kutta methods. Zbl 1347.65123Monovasilis, T.; Kalogiratou, Z.; Simos, T. E. 90 2016 On finite difference methods for the solution of the Schrödinger equation. Zbl 0940.65082Simos, T. E.; Williams, P. S. 89 1999 A Runge-Kutta type implicit high algebraic order two-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of coupled differential equations arising from the Schrödinger equation. Zbl 1318.65039Mu, Kenan; Simos, T. E. 88 2015 A family of high-order multistep methods with vanished phase-lag and its derivatives for the numerical solution of the Schrödinger equation. Zbl 1236.65083Alolyan, Ibraheem; Simos, T. E. 88 2011 Trigonometrically fitted Runge-Kutta methods for the numerical solution of the Schrödinger equation. Zbl 1070.81035Anastassi, Z. A.; Simos, T. E. 87 2005 A modified phase-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation. Zbl 1003.65082Simos, T. E.; Aguiar, Jesus Vigo 87 2001 New stable closed Newton-Cotes trigonometrically fitted formulae for long-time integration. Zbl 1242.65026Simos, T. E. 86 2012 Two optimized symmetric eight-step implicit methods for initial-value problems with oscillating solutions. Zbl 1198.81099Panopoulos, G. A.; Anastassi, Z. A.; Simos, T. E. 85 2009 A family of trigonometrically fitted partitioned Runge-Kutta symplectic methods. Zbl 1161.65090Monovasilis, Th.; Kalogiratou, Z.; Simos, T. E. 85 2009 A new two stage symmetric two-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of the radial Schrödinger equation. Zbl 1349.65222Zhou, Zhou; Simos, T. E. 84 2016 A new family of two stage symmetric two-step methods with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation. Zbl 1329.65142Hui, Fei; Simos, T. E. 83 2015 A new family of symmetric linear four-step methods for the efficient integration of the Schrödinger equation and related oscillatory problems. Zbl 1244.65107Alolyan, Ibraheem; Anastassi, Zacharias A.; Simos, Theodore E. 83 2012 Symmetric eighth algebraic order methods with minimal phase-lag for the numerical solution of the Schrödinger equation. Zbl 1002.65078Simos, T. E.; Vigo-Aguiar, Jesus 82 2002 Family of twelve steps exponential fitting symmetric multistep methods for the numerical solution of the Schrödinger equation. Zbl 1014.81055Vigo-Aguiar, J.; Simos, T. E. 81 2002 An optimized two-step hybrid block method for solving general second order initial-value problems. Zbl 1347.65121Ramos, Higinio; Kalogiratou, Z.; Monovasilis, Th.; Simos, T. E. 80 2016 Construction of trigonometrically and exponentially fitted Runge–Kutta–Nyström methods for the numerical solution of the Schrödinger equation and related problems – a method of 8th algebraic order. Zbl 1002.65077Kalogiratou, Z.; Simos, T. E. 80 2002 Exponentially-fitted Runge-Kutta-Nyström method for the numerical solution of initial-value problems with oscillating solutions. Zbl 1003.65081Simos, T. E. 76 2002 A family of exponentially-fitted Runge-Kutta methods with exponential order up to three for the numerical solution of the Schrödinger equation. Zbl 1125.81017Anastassi, Z. A.; Simos, T. E. 74 2007 A family of multiderivative methods for the numerical solution of the Schrödinger equation. Zbl 1070.81045Sakas, D. P.; Simos, T. E. 74 2005 Symplectic methods for the numerical solution of the radial Schrödinger equation. Zbl 1029.65134Tselios, Kostas; Simos, T. E. 73 2003 An eight-step semi-embedded predictor-corrector method for orbital problems and related IVPs with oscillatory solutions for which the frequency is unknown. Zbl 1330.65107Panopoulos, G. A.; Simos, T. E. 72 2015 A new explicit Bessel and Neumann fitted eighth algebraic order method for the numerical solution of the Schrödinger equation. Zbl 1014.81012Simos, T. E. 72 2000 New P-stable eighth algebraic order exponentially-fitted methods for the numerical integration of the Schrödinger equation. Zbl 1078.65061Avdelas, G.; Kefalidis, E.; Simos, T. E. 72 2002 Exponentially-fitted multiderivative methods for the numerical solution of the Schrödinger equation. Zbl 1050.65074Simos, T. E. 72 2004 A generator and an optimized generator of high-order hybrid explicit methods for the numerical solution of the Schrödinger equation. II: Development of the generator, optimization of the generator and numerical results. Zbl 1022.81009Avdelas, G.; Konguetsof, A.; Simos, T. E. 72 2001 Optimized Runge-Kutta pairs for problems with oscillating solutions. Zbl 1013.65073Tsitouras, Ch.; Simos, T. E. 71 2002 A generator and an optimized generator of high-order hybrid explicit methods for the numerical solution of the Schrödinger equation. I: Development of the basic method. Zbl 1022.81008Avdelas, G.; Konguetsof, A.; Simos, T. E. 71 2001 High order closed Newton-Cotes exponentially and trigonometrically fitted formulae as multilayer symplectic integrators and their application to the radial Schrödinger equation. Zbl 1403.81016Simos, T. E. 71 2012 A family of trigonometrically-fitted symmetric methods for the efficient solution of the Schrödinger equation and related problems. Zbl 1029.65079Simos, T. E. 70 2003 A new approach on the construction of trigonometrically fitted two step hybrid methods. Zbl 1382.65196Kalogiratou, Z.; Monovasilis, Th.; Ramos, Higinio; Simos, T. E. 70 2016 A low computational cost eight algebraic order hybrid method with vanished phase-lag and its first, second, third and fourth derivatives for the approximate solution of the Schrödinger equation. Zbl 1331.65098Ning, Hang; Simos, T. E. 69 2015 Exponentially fitted symplectic methods for the numerical integration of the Schrödinger equation. Zbl 1073.65071Monovasilis, Th.; Kalogiratou, Z.; Simos, T. E. 69 2005 Sixth algebraic order trigonometrically fitted predictor-corrector methods for the numerical solution of the radial Schrödinger equation. Zbl 1070.81044Psihoyios, G.; Simos, T. E. 69 2005 Trigonometrically fitted and exponentially fitted symplectic methods for the numerical integration of the Schrödinger equation. Zbl 1125.81021Monovasilis, Th.; Kalogiratou, Z.; Monovasilis, Th.; Simos, T. E. 67 2006 Multistage symmetric two-step P-stable method with vanished phase-lag and its first, second and third derivatives. Zbl 1332.65102Simos, Theodore E. 67 2015 New high order multiderivative explicit four-step methods with vanished phase-lag and its derivatives for the approximate solution of the Schrödinger equation. I: construction and theoretical analysis. Zbl 1270.81083Simos, T. E. 67 2013 Symplectic methods of fifth order for the numerical solution of the radial Schrödinger equation. Zbl 1044.81031Tselios, Kostas; Simos, T. E. 65 2004 An economical eighth-order method for the approximation of the solution of the Schrödinger equation. Zbl 1422.65115Wang, Zhiwei; Simos, T. E. 65 2017 An explicit four-step method with vanished phase-lag and its first and second derivatives. Zbl 1297.65084Simos, T. E. 64 2014 Two new optimized eight-step symmetric methods for the efficient solution of the Schrödinger equation and related problems. Zbl 1199.65236Panopoulos, G. A.; Anastassi, Z. A.; Simos, T. E. 63 2008 The numerical solution of the radial Schrödinger equation via a trigonometrically fitted family of seventh algebraic order predictor-corrector methods. Zbl 1125.81022Psihoyios, G.; Simos, T. E. 62 2006 An exponentially-fitted and trigonometrically-fitted method for the numerical solution of periodic initial-value problems. Zbl 1035.65071Konguetsof, A.; Simos, T. E. 62 2003 A dissipative exponentially-fitted method for the numerical solution of the Schrödinger equation and related problems. Zbl 1196.65123Simos, T. E.; Vigo-Aguiar, Jesus 62 2003 A four-step exponentially fitted method for the numerical solution of the Schrödinger equation. Zbl 1125.81023Simos, T. E. 61 2006 A Runge-Kutta type four-step method with vanished phase-lag and its first and second derivatives for each level for the numerical integration of the Schrödinger equation. Zbl 1300.65050Alolyan, Ibraheem; Simos, T. E. 59 2014 The use of phase lag and amplification error derivatives for the construction of a modified Runge-Kutta-Nyström method. Zbl 1275.65044Papadopoulos, D. F.; Simos, T. E. 58 2013 A finite difference pair with improved phase and stability properties. Zbl 1384.65050Yan, Ke; Simos, T. E. 58 2018 A family of two-stage two-step methods for the numerical integration of the Schrödinger equation and related IVPs with oscillating solution. Zbl 1198.81075Anastassi, Z. A.; Simos, T. E. 57 2009 An optimized explicit Runge-Kutta method with increased phase-lag order for the numerical solution of the Schrödinger equation and related problems. Zbl 1200.81052Kosti, A. A.; Anastassi, Z. A.; Simos, T. E. 57 2010 A high-order two-step phase-fitted method for the numerical solution of the Schrödinger equation. Zbl 1349.65221Zhang, Wei; Simos, T. E. 57 2016 A family of explicit linear six-step methods with vanished phase-lag and its first derivative. Zbl 1301.65068Alolyan, Ibraheem; Simos, T. E. 55 2014 A hybrid type four-step method with vanished phase-lag and its first, second and third derivatives for each level for the numerical integration of the Schrödinger equation. Zbl 1307.65106Alolyan, Ibraheem; Simos, T. E. 55 2014 A fourth algebraic order exponentially-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation. Zbl 0990.65079Simos, T. E. 55 2001 Efficient low computational cost hybrid explicit four-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical integration of the Schrödinger equation. Zbl 1325.65099Alolyan, Ibraheem; Simos, T. E. 54 2015 New second-order exponentially and trigonometrically fitted symplectic integrators for the numerical solution of the time-independent Schrödinger equation. Zbl 1132.81344Monovasilis, Th.; Simos, T. E. 54 2007 Symplectic partitioned Runge-Kutta methods with minimal phase-lag. Zbl 1219.65151Monovasilis, Th.; Kalogiratou, Z.; Simos, T. E. 54 2010 A new explicit hybrid four-step method with vanished phase-lag and its derivatives. Zbl 1297.65085Simos, T. E. 52 2014 High-order closed Newton-Cotes trigonometrically-fitted formulae for long-time integration of orbital problems. Zbl 1196.65194Simos, T. E. 50 2008 Closed Newton-Cotes trigonometrically-fitted formulae of high order for the numerical integration of the Schrödinger equation. Zbl 1217.65054Simos, T. E. 50 2008 Evolutionary generation of high-order, explicit, two-step methods for second-order linear IVPs. Zbl 1387.65066Simos, T. E.; Tsitouras, Ch. 50 2017 A family of four-step trigonometrically-fitted methods and its application to the Schrödinger equation. Zbl 1217.65139Simos, T. E. 49 2008 Explicit Numerov type methods with constant coefficients: a review. Zbl 1387.65065Simos, T. E.; Tsitouras, Ch.; Famelis, I. Th. 49 2017 Modified two-step hybrid methods for the numerical integration of oscillatory problems. Zbl 1383.65074Monovasilis, T.; Kalogiratou, Z.; Ramos, Higinio; Simos, T. E. 49 2017 Phase-fitted Runge-Kutta pairs of orders 8(7). Zbl 1366.65071Tsitouras, Ch.; Famelis, I. Th.; Simos, T. E. 49 2017 A new four stages symmetric two-step method with vanished phase-lag and its first derivative for the numerical integration of the Schrödinger equation. Zbl 1345.65048Liang, Minjian; Simos, T. E. 48 2016 Closed Newton-Cotes trigonometrically-fitted formulae for long-time integration. Zbl 1079.70502Simos, T. E. 48 2003 A symmetric eight-step predictor-corrector method for the numerical solution of the radial Schrödinger equation and related IVPs with oscillating solutions. Zbl 1262.65084Panopoulos, G. A.; Anastassi, Z. A.; Simos, T. E. 48 2011 A predictor-corrector explicit four-step method with vanished phase-lag and its first, second and third derivatives for the numerical integration of the Schrödinger equation. Zbl 1318.65042Alolyan, Ibraheem; Simos, T. E. 47 2015 A high algebraic order predictor-corrector explicit method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of the Schrödinger equation and related problems. Zbl 1331.65093Alolyan, Ibraheem; Simos, T. E. 47 2015 A high algebraic order multistage explicit four-step method with vanished phase-lag and its first, second, third, fourth and fifth derivatives for the numerical solution of the Schrödinger equation. Zbl 1325.65100Alolyan, Ibraheem; Simos, T. E. 47 2015 Some embedded modified Runge-Kutta methods for the numerical solution of some specific Schrödinger equations. Zbl 0915.65084Simos, T. E. 47 1998 Optimizing a hybrid two-step method for the numerical solution of the Schrödinger equation and related problems with respect to phase-lag. Zbl 1247.65096Simos, T. E. 47 2012 Closed Newton-Cotes trigonometrically-fitted formulae for the solution of the Schrödinger equation. Zbl 1199.65411Simos, T. E. 47 2008 A nonlinear explicit two-step fourth algebraic order method of order infinity for linear periodic initial value problems. Zbl 1219.65067Stavroyiannis, S.; Simos, T. E. 47 2010 A new symmetric eight-step predictor-corrector method for the numerical solution of the radial Schrödinger equation and related orbital problems. Zbl 1236.65085Panopoulos, G. A.; Anastassi, Z. A.; Simos, T. E. 46 2011 Computation of the eigenvalues of the Schrödinger equation by symplectic and trigonometrically fitted symplectic partitioned Runge-Kutta methods. Zbl 1217.81061Monovasilis, Th.; Kalogiratou, Z.; Simos, T. E. 44 2008 A new optimized symmetric 8-step semi-embedded predictor-corrector method for the numerical solution of the radial Schrödinger equation and related orbital problems. Zbl 1312.65117Panopoulos, G. A.; Simos, T. E. 44 2013 A new methodology for the construction of optimized Runge-Kutta-Nyström methods. Zbl 1262.65080Papadopoulos, D. F.; Simos, T. E. 44 2011 A singularly P-stable two-step method with improved characteristics for problems in chemistry. Zbl 1484.81032Medvedeva, Marina A.; Simos, T. E. 4 2022 A two-step singularly P-Stable method with high phase and large stability properties for problems in chemistry. Zbl 1487.81083Generalov, Dmitry; Tsvetova, Ekaterina; Fedorov, Ruslan; Kovalnogov, Vladislav; Simos, T. E. 2 2022 A phase-fitting and first derivative phase-fitting singularly P-stable economical two-step method for problems in quantum chemistry. Zbl 07562014Medvedev, Maxim A.; Simos, T. E. 2 2022 A two-step method singularly P-Stable with improved properties for problems in quantum chemistry. Zbl 1487.81087Medvedeva, Marina A.; Simos, T. E. 1 2022 A new economical method with eliminated phase-lag and its derivative for problems in chemistry. Zbl 1466.65048Ma, Yu-Yu; Lin, Chia-Liang; Simos, T. E. 6 2021 A new method with improved phase-lag and stability properties for problems in quantum chemistry - an economical case. Zbl 07382634Li, Xingyuan; Lin, Chia-Liang; Simos, T. E. 3 2021 An economical two-step method with improved phase and stability properties for problems in chemistry. Zbl 1472.65084Medvedeva, Marina A.; Simos, T. E. 3 2021 A new improved economical finite difference method for problems in quantum chemistry. Zbl 1472.65085Mingliang, Zheng; Simos, T. E. 3 2021 Two-step method with vanished phase-lag and its derivatives for problems in quantum chemistry: an economical case. Zbl 1476.81166Medvedev, Maxim A.; Simos, T. E. 1 2021 An economical two-step method with optimal phase and stability properties for problems in chemistry. Zbl 1476.81165Medvedeva, Marina A.; Simos, T. E. 1 2021 A phase fitted FinDiff process for DifEquns in quantum chemistry. Zbl 1433.81079Hao, Sheng; Simos, T. E. 24 2020 An integrated in phase FD procedure for DiffEqns in chemical problems. Zbl 1433.81081Ma, Yu-Yu; Lin, Chia-Liang; Simos, T. E. 19 2020 A complete in phase FinitDiff procedure for DiffEquns in chemistry. Zbl 1433.81168Tong, Xing; Simos, T. E. 19 2020 A phase fitted FiniteDiffr process for DiffrntEqutns in chemistry. Zbl 1440.65283Chen, Xiaoping; Simos, T. E. 15 2020 A complete in phase FiniteDiffrnc algorithm for DiffrntEqutins in chemistry. Zbl 1440.65284Lin, Chia-Liang; Simos, T. E. 12 2020 Full in phase finite difference algorithm for differential equations in quantum chemistry. Zbl 1440.65285Zhao, Zhen; Luo, Jun; Lin, Chia-Liang; Simos, T. E. 12 2020 Neural network solution of pantograph type differential equations. Zbl 1453.65165Hou, Chih-Chun; Simos, Theodore E.; Famelis, Ioannis Th. 9 2020 Neural network solution of single-delay differential equations. Zbl 1431.65090Fang, Jie; Liu, Chenglian; Simos, T. E.; Famelis, I. Th. 7 2020 Phase fitted method for quantum chemistry problems. Zbl 1444.81038Luo, Jun; Zhao, Zhen; Lin, Chia-Liang; Simos, T. E. 5 2020 Complete in phase method for problems in chemistry. Zbl 1471.65089Lin, Chia-Liang; Simos, T. E. 4 2020 Phase fitted algorithm for problems in quantum chemistry. Zbl 1448.81484Medvedeva, Marina A.; Simos, T. E. 3 2020 A finite difference method with zero phase-lag and its derivatives for quantum chemistry problems. Zbl 1448.81315Wang, Zenggui; Simos, T. E. 3 2020 A finite difference method with phase-lag and its derivatives equal to zero for problems in chemistry. Zbl 1448.65076Medvedev, Maxim A.; Simos, T. E. 3 2020 Variable step-size implementation of sixth-order Numerov-type methods. Zbl 1451.65087Medvedeva, Marina A.; Simos, Theodore E.; Tsitouras, Charalampos 2 2020 Two-derivative Runge-Kutta methods with optimal phase properties. Zbl 1452.65123Kalogiratou, Zacharoula; Monovasilis, Theodore; Simos, Theodore E. 2 2020 Trigonometric fitted modification of RADAU5. Zbl 1451.65083Medvedeva, Marina A.; Simos, Theodore E.; Tsitouras, Charalampos 2 2020 Eighth-order, phase-fitted, four-step methods for solving \(y^{\prime \prime} = f(x, y)\). Zbl 1453.65156Alolyan, Ibraheem; Simos, Theodore E.; Tsitouras, Charalampos 2 2020 Ninth-order, explicit, two-step methods for second-order inhomogeneous linear IVPs. Zbl 1451.65086Kovalnogov, Vladislav N.; Simos, Theodore E.; Tsitouras, Charalampos 2 2020 Explicit, ninth order, two step methods for solving inhomogeneous linear problems \(x''(t)= \Lambda x(t)+f(t)\). Zbl 1436.65085Simos, T. E.; Tsitouras, Ch. 2 2020 Explicit, eighth-order, four-step methods for solving \(y^{\prime\prime}=f(x, y)\). Zbl 1450.65063Medvedev, Maxim A.; Simos, T. E.; Tsitouras, Ch. 1 2020 6th order Runge-Kutta pairs for scalar autonomous IVP. Zbl 1480.65176Simos, T. E.; Tsitouras, Ch. 1 2020 A three-stages multistep teeming in phase algorithm for computational problems in chemistry. Zbl 1417.81172Medvedev, Maxim A.; Simos, T. E. 35 2019 An accomplished phase FD process for DEs in chemistry. Zbl 1429.81028Medvedeva, Marina A.; Simos, T. E. 27 2019 A multistage two-step fraught in phase scheme for problems in mathematical chemistry. Zbl 1436.65086Xu, Mingfei; Simos, T. E. 25 2019 A Runge-Kutta type crowded in phase algorithm for quantum chemistry problems. Zbl 1422.81180Lv, Jieyin; Simos, T. E. 20 2019 Trigonometric-fitted hybrid four-step methods of sixth order for solving \(y''(x)= f(x,y)\). Zbl 1410.65254Medvedev, Maxim A.; Simos, T. E.; Tsitouras, Ch. 19 2019 A multiple stage absolute in phase scheme for chemistry problems. Zbl 1426.81059Zhang, Xunying; Simos, T. E. 17 2019 A perfect in phase FD algorithm for problems in quantum chemistry. Zbl 1426.81058Qiu, Junlai; Huang, Junjie; Simos, T. E. 15 2019 New multiple stages two-step complete in phase algorithm with improved characteristics for second order initial/boundary value problems. Zbl 1414.81100Wang, Guiping; Simos, T. E. 13 2019 Hybrid, phase-fitted, four-step methods of seventh order for solving \(x''(t) = f(t,x)\). Zbl 1416.65195Medvedev, Maxim A.; Simos, T. E.; Tsitouras, Ch. 13 2019 Evolutionary derivation of sixth-order P-stable SDIRKN methods for the solution of PDEs with the method of lines. Zbl 1415.65150Lin, Chialiang; Chen, Jwu Jenq; Simos, T. E.; Tsitouras, Ch. 13 2019 Hybrid Numerov-type methods with coefficients trained to perform better on classical orbits. Zbl 1437.65067Liu, Chenglian; Hsu, Chieh-Wen; Tsitouras, Ch.; Simos, T. E. 10 2019 A new multistep method with optimized characteristics for initial and/or boundary value problems. Zbl 1406.81027Qiu, Guo-Hua; Liu, Chenglian; Simos, T. E. 10 2019 New fifth-order two-derivative Runge-Kutta methods with constant and frequency-dependent coefficients. Zbl 1416.65194Kalogiratou, Zacharoula; Monovasilis, Theodore; Simos, Theodore E. 10 2019 Explicit hybrid six – step, sixth order, fully symmetric methods for solving \(y"=f(x,y)\). Zbl 07082219Fang, Jie; Liu, Chenglian; Hsu, Chieh-wen; Simos, Theodore E.; Tsitouras, Charalampos 8 2019 Phase-fitted, six-step methods for solving \(x^{\prime\prime} = f(t,x)\). Zbl 1431.65111Liu, Chenglian; Hsu, Chieh-Wen; Simos, T. E.; Tsitouras, Ch. 7 2019 New multistage two-step complete in phase scheme with improved properties for quantum chemistry problems. Zbl 1414.81088Hui, Fei; Simos, T. E. 7 2019 A new multistage multistep full in phase algorithm with optimized characteristics for problems in chemistry. Zbl 1414.81279Chen, Zhong; Liu, Chenglian; Hsu, Chieh-Wen; Simos, T. E. 7 2019 A four-stages multistep fraught in phase method for quantum chemistry problems. Zbl 1417.81170Alolyan, Ibraheem; Simos, T. E. 7 2019 New four stages multistep in phase algorithm with best possible properties for second order problems. Zbl 1414.81101Yang, Nan; Simos, T. E. 6 2019 A new four-stages two-step phase fitted scheme for problems in quantum chemistry. Zbl 1414.81281Hsu, Chieh-Wen; Lin, Chialiang; Liu, Chenglian; Simos, T. E. 6 2019 Low-order, P-stable, two-step methods for use with lax accuracies. Zbl 1431.65097Medvedev, Maxim A.; Simos, Theodore E.; Tsitouras, Charalampos 6 2019 Local interpolants for Numerov-type methods and their implementation in variable step schemes. Zbl 1431.65098Medvedev, Maxim A.; Simos, Theodore E.; Tsitouras, Charalampos 5 2019 Interpolants for sixth-order Numerov-type methods. Zbl 1431.65094Alolyan, Ibraheem; Simos, T. E.; Tsitouras, Ch. 5 2019 Explicit, semi-symmetric, hybrid, six-step, eighth order methods for solving \(y''=f(x,y)\). Zbl 1431.65096Lin, Chialiang; Hsu, Chieh-Wen; Simos, T. E.; Tsitouras, Ch. 5 2019 New multiple stages scheme with improved properties for second order problems. Zbl 1406.81026Kovalnogov, V. N.; Fedorov, R. V.; Suranov, D. V.; Simos, T. E. 1 2019 New multiple stages multistep method with best possible phase properties for second order initial/boundary value problems. Zbl 1414.81083Alolyan, Ibraheem; Simos, T. E. 1 2019 A finite difference pair with improved phase and stability properties. Zbl 1384.65050Yan, Ke; Simos, T. E. 58 2018 Trigonometric fitted, eighth-order explicit Numerov-type methods. Zbl 1387.65061Berg, Dmitry B.; Simos, T. E.; Tsitouras, Ch. 33 2018 On ninth order, explicit Numerov-type methods with constant coefficients. Zbl 1446.65046Tsitouras, Ch.; Simos, T. E. 27 2018 Trigonometric-fitted explicit Numerov-type method with vanishing phase-lag and its first and second derivatives. Zbl 1402.65063Tsitouras, Ch.; Simos, T. E. 27 2018 Fitted modifications of classical Runge-Kutta pairs of orders 5(4). Zbl 1405.65087Simos, T. E.; Tsitouras, Ch. 25 2018 A four stages numerical pair with optimal phase and stability properties. Zbl 1384.65048Kovalnogov, Vladislav N.; Fedorov, Ruslan V.; Golovanov, Viktor M.; Kostishko, Boris M.; Simos, T. E. 25 2018 Explicit, two-stage, sixth-order, hybrid four-step methods for solving \(y''=(x)=f(x,y)\). Zbl 1402.65058Medvedev, Maxim A.; Simos, T. E.; Tsitouras, Ch. 21 2018 Fitted modifications of Runge-Kutta pairs of orders 6(5). Zbl 1402.65057Medvedev, Maxim A.; Simos, T. E.; Tsitouras, Ch. 20 2018 New finite difference pair with optimized phase and stability properties. Zbl 1453.65162Yao, Junfeng; Simos, T. E. 19 2018 New five-stages two-step method with improved characteristics. Zbl 1397.81068Yao, Junfeng; Simos, T. E. 18 2018 New three-stages symmetric two step method with improved properties for second order initial/boundary value problems. Zbl 1411.65086Chen, Zhong; Liu, Chenglian; Simos, T. E. 18 2018 A new two-step finite difference pair with optimal properties. Zbl 1474.65219Zheng, Jinbin; Liu, Chenglian; Simos, T. E. 18 2018 New five-stages finite difference pair with optimized phase properties. Zbl 1447.81118Shi, Xin; Simos, T. E. 18 2018 A five-stages symmetric method with improved phase properties. Zbl 1479.81019Liu, Chenglian; Simos, T. E. 18 2018 A hybrid finite difference pair with maximum phase and stability properties. Zbl 1453.65158Fang, Jie; Liu, Chenglian; Simos, T. E. 17 2018 New hybrid two-step method with optimized phase and stability characteristics. Zbl 1402.81137Kovalnogov, V. N.; Fedorov, R. V.; Bondarenko, A. A.; Simos, T. E. 17 2018 Trigonometrical fitting conditions for two derivative Runge-Kutta methods. Zbl 1416.65207Monovasilis, Th.; Kalogiratou, Z.; Simos, T. E. 16 2018 New Runge-Kutta type symmetric two-step method with optimized characteristics. Zbl 1402.81145Yan, Ke; Simos, T. E. 16 2018 New Runge-Kutta type symmetric two step finite difference pair with improved properties for second order initial and/or boundary value problems. Zbl 1406.81025Hao, Ruru; Simos, T. E. 11 2018 New hybrid symmetric two step scheme with optimized characteristics for second order problems. Zbl 1411.65087Kovalnogov, V. N.; Fedorov, R. V.; Simos, T. E. 10 2018 High phase-lag order, four-step methods for solving \(y^{\prime\prime} = f(x, y)\). Zbl 1432.65094Simos, T. E.; Tsitouras, Ch. 10 2018 A multistep method with optimal properties for second order differential equations. Zbl 1384.65049Medvedev, Maxim A.; Simos, T. E. 7 2018 A new multistep finite difference pair for the Schrödinger equation and related problems. Zbl 1462.65079Berg, Dmitriy B.; Simos, T. E. 3 2018 A new six-step algorithm with improved properties for the numerical solution of second order initial and/or boundary value problems. Zbl 1447.81113Medvedev, Maxim A.; Simos, T. E. 3 2018 New four-stages symmetric six-step method with improved phase properties for second order problems with periodical and/or oscillating solutions. Zbl 1425.65072Alolyan, Ibraheem; Simos, T. E. 2 2018 A new three-stages six-step finite difference pair with optimal phase properties for second order initial and/or boundary value problems with periodical and/or oscillating solutions. Zbl 1447.81114Medvedev, Maxim A.; Simos, T. E. 2 2018 New 8-step symmetric embedded predictor-corrector (EPCM) method with vanished phase-lag and its first derivative for the numerical integration of the Schrödinger equation. Zbl 1411.81088Stasinos, P. I.; Simos, Theodore E. 1 2018 New three-stages symmetric six-step finite difference method with vanished phase-lag and its derivatives up to sixth derivative for second order initial and/or boundary value problems with periodical and/or oscillating solutions. Zbl 1402.81123Alolyan, Ibraheem; Simos, T. E. 1 2018 An economical eighth-order method for the approximation of the solution of the Schrödinger equation. Zbl 1422.65115Wang, Zhiwei; Simos, T. E. 65 2017 Evolutionary generation of high-order, explicit, two-step methods for second-order linear IVPs. Zbl 1387.65066Simos, T. E.; Tsitouras, Ch. 50 2017 Explicit Numerov type methods with constant coefficients: a review. Zbl 1387.65065Simos, T. E.; Tsitouras, Ch.; Famelis, I. Th. 49 2017 Modified two-step hybrid methods for the numerical integration of oscillatory problems. Zbl 1383.65074Monovasilis, T.; Kalogiratou, Z.; Ramos, Higinio; Simos, T. E. 49 2017 Phase-fitted Runge-Kutta pairs of orders 8(7). Zbl 1366.65071Tsitouras, Ch.; Famelis, I. Th.; Simos, T. E. 49 2017 A new family of 7 stages, eighth-order explicit Numerov-type methods. Zbl 1387.65067Simos, T. E.; Tsitouras, Ch. 41 2017 An efficient and computational effective method for second order problems. Zbl 1422.65113Ma, Jing; Simos, T. E. 33 2017 An efficient and economical high order method for the numerical approximation of the Schrödinger equation. Zbl 1383.65083Yang, Lan; Simos, T. E. 21 2017 A new two stages tenth algebraic order symmetric six-step method with vanished phase-lag and its first and second derivatives for the solution of the radial Schrödinger equation and related problems. Zbl 1359.65105Alolyan, Ibraheem; Simos, T. E. 13 2017 Two stages six-step method with eliminated phase-lag and its first, second, third and fourth derivatives for the approximation of the Schrödinger equation. Zbl 1383.65080Medvedev, Maxim A.; Simos, T. E. 11 2017 New two stages high order symmetric six-step method with vanished phase-lag and its first, second and third derivatives for the numerical solution of the Schrödinger equation. Zbl 1384.65047Alolyan, Ibraheem; Simos, T. E. 11 2017 High order computationally economical six-step method with vanished phase-lag and its derivatives for the numerical solution of the Schrödinger equation. Zbl 1383.65078Berg, Dmitriy B.; Simos, T. E. 10 2017 Three stages symmetric six-step method with eliminated phase-lag and its derivatives for the solution of the Schrödinger equation. Zbl 1422.65111Berg, Dmitriy B.; Simos, T. E. 10 2017 An efficient six-step method for the solution of the Schrödinger equation. Zbl 1422.65112Berg, Dmitriy B.; Simos, T. E. 8 2017 A new fourteenth algebraic order finite difference method for the approximate solution of the Schrödinger equation. Zbl 1422.65329Zhao, Jianbin; Simos, T. E. 1 2017 ...and 270 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 596 Authors 252 Simos, Theodore E. 30 Alolyan, Ibraheem 30 Fang, Yonglei 30 Tsitouras, Charalampos 26 You, Xiong 24 Vigo-Aguiar, Jesus 23 Wu, Xinyuan 21 Anastassi, Zacharias A. 21 Ramos, Higinio 19 Franco, J. Méndez 16 Ismail, Fudziah Bt. 16 Senu, Norazak 15 Van Daele, Marnix 15 Van de Vyver, Hans 15 Vanden Berghe, Guido 14 Kalogiratou, Zacharoula 14 Lin, Chialiang 14 Rández, Luis 13 Medvedev, Maxim A. 12 Li, Jiyong 12 Paternoster, Beatrice 12 Wang, Bin 11 Ixaru, Liviu Gr. 11 Jator, Samuel N. 11 Wang, Zhongcheng 9 Calvo, Manuel 9 Konguetsof, Avrilia 9 Liu, Chenglian 8 De Meyer, Hans E. 8 Khalsaraei, Mohammad Mehdizadeh 8 Li, Qinghong 8 Yang, Yanping 7 Dai, Yongming 7 Famelis, Ioannis Th. 7 Medvedeva, Marina A. 7 Montijano, Juan Ignacio 7 Suleiman, Mohamed Bin 6 D’Ambrosio, Raffaele 6 Panopoulos, G. A. 6 Shi, Wei 6 Vlachos, D. S. 6 Zheng, Juan 5 Ahmad, Sufia Zulfa 5 Avdelas, George 5 Chen, Bingzhen 5 Chen, Zhaoxia 5 Fedorov, Ruslan V. 5 Garcia-Rubio, Raquel 5 Kosti, Athinoula A. 5 Kovalnogov, Vladislav N. 5 Liu, Shiwei 5 Ming, Qinghe 5 Monovasilis, Theodoros 5 Ngwane, Fidele F. 5 Okunuga, Solomon A. 5 Papageorgiou, George 5 Singh, Gurjinder 5 Zhai, Wenjuan 4 Berg, Dmitry B. 4 Conte, Dajana 4 Erdoğan, Utku 4 Kalvouridis, Tilemahos J. 4 Martín-Vaquero, Jesús 4 Ozawa, Kazufumi 4 Witwit, M. R. M. 4 Yang, Hongli 3 Abdulganiy, Ridwanulahi Iyanda 3 Brugnano, Luigi 3 Ding, Peizhu 3 Ehigie, Julius Osato 3 Esposito, Elena 3 García Guirao, Juan Luis 3 Hsu, Chieh-Wen 3 Iavernaro, Felice 3 Khan, Ishtiaq Rasool 3 Liu, Xueshen 3 Mohanty, Ranjan Kumar 3 Neta, Beny 3 Ohba, Ryoji 3 Papadopoulos, D. F. 3 Rufai, Mufutau Ajani 3 Sakas, D. P. 3 Sideridis, A. B. 3 Wang, Zenggui 3 Williams, P. S. 3 Wu, Dongmei 3 Yildirim, Ozgur 3 Zhang, Yanwei 2 Achar, Sujatha D. 2 Ahmad, Nur Amirah 2 Akinfenwa, Olusheye Aremu Akin 2 Alonso, Pedro 2 Alvarez, Jorge 2 Biswas, Amitava 2 Chen, Zhanqing 2 Chen, Zhong 2 Dai, Weizhong 2 Deb, Anish 2 Demiralp, Metin 2 Deng, Shuo ...and 496 more Authors all top 5 Cited in 100 Serials 187 Journal of Mathematical Chemistry 87 Journal of Computational and Applied Mathematics 75 Applied Mathematics and Computation 45 Computer Physics Communications 31 Computers & Mathematics with Applications 26 Numerical Algorithms 21 International Journal of Modern Physics C 20 Applied Numerical Mathematics 20 International Journal of Computer Mathematics 15 Journal of Computational Physics 12 Applied Mathematics Letters 12 Mathematical Problems in Engineering 11 Mathematical and Computer Modelling 11 Abstract and Applied Analysis 9 Discrete Dynamics in Nature and Society 9 Mediterranean Journal of Mathematics 8 Japan Journal of Industrial and Applied Mathematics 8 Journal of Applied Mathematics 6 Computational and Applied Mathematics 5 Journal of the Nigerian Mathematical Society 4 Molecular Simulation 4 Journal of Applied Mathematics and Computing 3 Calcolo 3 Mathematics and Computers in Simulation 2 Astrophysics and Space Science 2 Computer Methods in Applied Mechanics and Engineering 2 Journal of Mathematical Physics 2 Mathematical Methods in the Applied Sciences 2 Chaos, Solitons and Fractals 2 BIT 2 Applied Mathematical Modelling 2 Journal of the Egyptian Mathematical Society 2 Engineering Analysis with Boundary Elements 2 Far East Journal of Applied Mathematics 2 Communications in Nonlinear Science and Numerical Simulation 2 Bulletin of the Malaysian Mathematical Sciences Society. 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