Edit Profile (opens in new tab) Vanden Berghe, Guido Co-Author Distance Author ID: vanden-berghe.guido Published as: Vanden Berghe, G.; Vanden Berghe, Guido; vanden Berghe, G.; Van den Berghe, G.; Berghe, Guido Vanden more...less External Links: Wikidata · GND · IdRef Documents Indexed: 147 Publications since 1976, including 2 Books 5 Contributions as Editor Reviewing Activity: 37 Reviews Co-Authors: 29 Co-Authors with 149 Joint Publications 727 Co-Co-Authors all top 5 Co-Authors 3 single-authored 95 De Meyer, Hans E. 64 Van Daele, Marnix 15 Van der Jeugt, Joris 14 Ixaru, Liviu Gr. 13 Ledoux, Veerle 13 Vanthournout, Jan 10 Van Hecke, Tanja 7 Fack, Veerle 6 Bocher, Philippe 6 Srinivasa Rao, K. 5 Dewilde, Patrick M. 5 Hollevoet, D. 5 Rizea, M. 4 Van de Vyver, Hans 3 Hughes, J. W. B. 2 Baker, Christopher Thomas Hale 2 Kota, V. K. B. 2 Monegato, Giovanni 2 Pryce, John D. 2 Van Assche, Walter 1 Bulatov, Mikhail Valer’yanovich 1 Carjan, Nicolae 1 Chakrabarti, Aloknath 1 Devreese, Jozef T. 1 Kanemitsu, Shigeru 1 Krattenthaler, Christian Friedrich 1 Niyokindi, C. 1 Silişteanu, I. 1 Vigo-Aguiar, Jesus all top 5 Serials 34 Journal of Computational and Applied Mathematics 27 Journal of Mathematical Physics 14 Computer Physics Communications 11 Journal of Physics A: Mathematical and General 9 Computers & Mathematics with Applications 9 International Journal of Computer Mathematics 8 Applied Numerical Mathematics 4 Numerical Algorithms 2 Numerische Mathematik 2 ANACM. Applied Numerical Analysis and Computational Mathematics 1 IMA Journal of Numerical Analysis 1 International Journal of Theoretical Physics 1 Physica A 1 Physics Letters. A 1 ACM Transactions on Mathematical Software 1 Gaṇita-Bhāratī 1 Applied Mathematics Letters 1 Historia Scientiarum. Second Series 1 Annals of Physics 1 Numerical Linear Algebra with Applications 1 Journal of Computational Methods in Sciences and Engineering 1 Mathematics and its Applications (Dordrecht) 1 JNAIAM. Journal of Numerical Analysis, Industrial and Applied Mathematics all top 5 Fields 95 Numerical analysis (65-XX) 66 Ordinary differential equations (34-XX) 48 Quantum theory (81-XX) 34 Topological groups, Lie groups (22-XX) 13 Nonassociative rings and algebras (17-XX) 12 Special functions (33-XX) 8 Approximations and expansions (41-XX) 5 General and overarching topics; collections (00-XX) 5 History and biography (01-XX) 5 Integral equations (45-XX) 3 Dynamical systems and ergodic theory (37-XX) 2 Group theory and generalizations (20-XX) 2 Sequences, series, summability (40-XX) 1 Real functions (26-XX) 1 Partial differential equations (35-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Operator theory (47-XX) 1 Computer science (68-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 127 Publications have been cited 1,901 times in 703 Documents Cited by ▼ Year ▼ Exponential fitting. With CD-ROM. Zbl 1105.65082 Ixaru, Liviu Gr.; Vanden Berghe, Guido 110 2004 Frequency evaluation in exponential fitting multistep algorithms for ODEs. Zbl 0996.65075 Ixaru, L. Gr.; Vanden Berghe, G.; De Meyer, H. 103 2002 Exponentially-fitted explicit Runge-Kutta methods. Zbl 0948.65066 Vanden Berghe, G.; De Meyer, H.; Van Daele, M.; Van Hecke, T. 95 1999 Exponentially fitted Runge-Kutta methods. Zbl 0999.65065 Vanden Berghe, G.; De Meyer, H.; Van Daele, M.; Van Hecke, T. 69 2000 Exponentially fitted variable two-step BDF algorithm for first order ODEs. Zbl 1196.65110 Ixaru, L. Gr.; Vanden Berghe, Guido; De Meyer, Hans 64 2003 P-stable exponentially-fitted Obrechkoff methods of arbitrary order for second-order differential equations. Zbl 1134.65043 Van Daele, M.; Vanden Berghe, G. 61 2007 Weights of the exponential fitting multistep algorithms for first-order ODEs. Zbl 0991.65061 Ixaru, L. Gr.; Rizea, M.; Vanden Berghe, G.; De Meyer, H. 60 2001 The optimal exponentially-fitted Numerov method for solving two-point boundary value problems. Zbl 1167.65406 Hollevoet, D.; Van Daele, M.; Vanden Berghe, G. 58 2009 Four-step exponential-fitted methods for nonlinear physical problems. Zbl 0927.65100 Ixaru, L. Gr.; Vanden Berghe, G.; De Meyer, H.; Van Daele, M. 52 1997 Exponentially-fitted Obrechkoff methods for second-order differential equations. Zbl 1166.65352 Vanden Berghe, G.; Van Daele, M. 50 2009 \(P\)-stable Obrechkoff methods of arbitrary order for second-order differential equations. Zbl 1123.65070 Van Daele, Marnix; Vanden Berghe, Guido 49 2007 EXPFIT4 – a FORTRAN program for the numerical solution of systems of nonlinear second-order initial-value problems. Zbl 0927.65099 Ixaru, L. Gr.; De Meyer, H.; Vanden Berghe, G.; Van Daele, M. 49 1997 Exponential-fitted four-step methods for \(y''=f(x,y)\). Zbl 0894.65032 Van Daele, M.; Vanden Berghe, G.; De Meyer, H.; Ixaru, L. Gr. 47 1998 Properties and implementation of \(r\)-Adams methods based on mixed-type interpolation. Zbl 0837.65079 Van Daele, M.; Vanden Berghe, G.; De Meyer, H. 46 1995 Finite difference approach for the two-dimensional Schrödinger equation with application to scission-neutron emission. Zbl 1197.81041 Rizea, M.; Ledoux, V.; Van Daele, M.; Vanden Berghe, G.; Carjan, N. 44 2008 On a new type of mixed interpolation. Zbl 0693.41003 De Meyer, H.; Vanthournout, J.; Vanden Berghe, G. 44 1990 MATSLISE: a MATLAB package for the numerical solution of Sturm-Liouville and Schrödinger equations. Zbl 1136.65327 Ledoux, Veerle; Van Daele, Marnix; Vanden Berghe, Guido 42 2005 Frequency determination and step-length control for exponentially-fitted Runge-Kutta methods. Zbl 0991.65062 Vanden Berghe, G.; Ixaru, L. Gr.; De Meyer, H. 35 2001 On the error estimation for a mixed type of interpolation. Zbl 0725.41002 De Meyer, H.; Vanthournout, J.; Van den Berghe, G. 32 1990 Exponential fitted Runge-Kutta methods of collocation type: Fixed or variable knot points? Zbl 1031.65084 Vanden Berghe, G.; Van Daele, M.; Vande Vyver, H. 31 2003 Optimal implicit exponentially-fitted Runge-Kutta methods. Zbl 0990.65080 Vanden Berghe, G.; Ixaru, L. Gr.; Van Daele, M. 29 2001 A modified Numerov integration method for second order periodic initial- value problems. Zbl 0752.65059 Vanden Berghe, G.; De Meyer, H.; Vanthournout, J. 23 1990 A smooth approximation for the solution of a fourth-order boundary value problem based on nonpolynomial splines. Zbl 0810.65079 van Daele, M.; vanden Berghe, G.; de Meyer, H. 22 1994 A finite difference approach for the calculation of perturbed oscillator energies. Zbl 0584.65055 Fack, V.; Vanden Berghe, G. 21 1985 On a class of modified Newton-Cotes quadrature formulae based upon mixed- type interpolation. Zbl 0729.41032 Vanden Berghe, G.; De Meyer, H.; Vanthournout, J. 21 1990 Exponentially-fitted Numerov methods. Zbl 1110.65071 Vanden Berghe, G.; Van Daele, M. 19 2007 Numerical methods for solving radial Schrödinger equations. Zbl 0694.65033 Vanden Berghe, G.; Fack, V.; De Meyer, H. E. 19 1989 Families of backward differentiation methods based on a new type of mixed interpolation. Zbl 0752.65060 Vanthournout, Jan; Vanden Berghe, Guido; De Meyer, Hans 18 1990 Dynamic-group approach to the \(x^ 2+\lambda x^ 2/(1+gx^ 2)\) potential. Zbl 0603.22007 Fack, V.; de Meyer, H.; Vanden Berghe, G. 18 1986 Exponentially-fitted Störmer/Verlet methods. Zbl 1127.65050 Vanden Berghe, G.; Van Daele, M. 17 2006 CP methods for the Schrödinger equation revisited. Zbl 0909.65045 Ixaru, L. Gr.; De Meyer, H.; Vanden Berghe, G. 16 1998 Approximate solution of singular integral equations. Zbl 1061.65141 Chakrabarti, A.; Vanden Berghe, G. 15 2004 Geometric numerical integration by means of exponentially-fitted methods. Zbl 1116.65125 Van Daele, M.; Vanden Berghe, G. 15 2007 SLCPM12 – a program for solving regular Sturm-Liouville problems. Zbl 1008.34016 Ixaru, L. Gr.; De Meyer, H.; Vanden Berghe, G. 14 1999 Accurate computation of higher Sturm-Liouville eigenvalues. Zbl 0716.65079 Vanden Berghe, G.; De Meyer, H. 14 1991 A modified Numerov method for higher Sturm-Liouville eigenvalues. Zbl 0726.65100 Vanden Berghe, G.; de Meyer, H. 14 1990 Shift operator techniques for the classification of multipole-phonon states. VII: Self-consistent single step algorithm for R(5) \(O^0\) eigenstate and eigenvalue determination. Zbl 0444.22015 De Meyer, H. E.; Vanden Berghe, G. 13 1980 (Extended) Numerov method for computing eigenvalues of specific Schrödinger equations. Zbl 0626.65079 Fack, V.; Vanden Berghe, G. 13 1987 Exponentially fitted methods applied to fourth-order boundary value problems. Zbl 1225.65075 Hollevoet, D.; Van Daele, M.; Vanden Berghe, G. 12 2011 CP methods of higher order for Sturm-Liouville and Schrödinger equations. Zbl 1196.65131 Ledoux, V.; Van Daele, M.; Vanden Berghe, Guido 11 2004 On a correction of Numerov-like eigenvalue approximations for Sturm- Liouville problems. Zbl 0753.65071 Vanden Berghe, G.; de Meyer, H. 11 1991 Some finite difference methods for computing eigenvalues and eigenvectors of special two-point boundary value problems. Zbl 0635.65101 Fack, V.; Vanden Berghe, G.; De Meyer, H. E. 11 1987 Realizations of \(F_ 4\) in \(\text{SO}(3)\otimes\text{SO}(3)\) bases and structural zeros of the \(6j\)-symbol. Zbl 0551.22008 De Meyer, Hans; Vanden Berghe, G.; Van der Jeugt, Joris 10 1984 Symplectic exponentially-fitted four-stage Runge-Kutta methods of the Gauss type. Zbl 1215.65130 Vanden Berghe, Guido; Van Daele, Marnix 9 2011 A parallel approach to the modified Numerov-like eigenvalue determination for Sturm-Liouville problems. Zbl 0773.65066 Vanden Berghe, G.; De Meyer, H.; Van Daele, M. 9 1992 Exponentially fitted quadrature rules of Gauss type for oscillatory integrands. Zbl 1069.65022 Van Daele, M.; Vanden Berghe, G.; Vande Vyver, H. 9 2005 A modified difference scheme for periodic and semiperiodic Sturm- Liouville problems. Zbl 0834.65075 Vanden Berghe, G.; Van Daele, M.; De Meyer, H. 9 1995 Shift-operator techniques for the classification of multipole-phonon states. I: Properties of shift operators in the \(R(5)\) group. Zbl 0444.22009 Vanden Berghe, G.; De Meyer, H. E. 9 1980 On a class of \(P\)-stable mono-implicit Runge-Kutta-Nyström methods. Zbl 0937.65085 Van Daele, M.; De Meyer, H.; Van Hecke, T.; Vanden Berghe, G. 9 1998 Efficient computation of high index Sturm-Liouville eigenvalues for problems in physics. Zbl 1198.65124 Ledoux, V.; Van Daele, M.; Vanden Berghe, Guido 8 2009 On Gregory-and modified Gregory-type corrections to Newton-Cotes quadrature. Zbl 0808.41020 Bocher, P.; de Meyer, H.; vanden Berghe, G. 8 1994 Multistep methods for ordinary differential equations based on algebraic and first order trigonometric polynomials. Zbl 0768.65044 Vanthournout, J.; De Meyer, H.; Vanden Berghe, G. 8 1992 Extended one-step methods: An exponential fitting approach. Zbl 1063.65063 Van Daele, M.; Vanden Berghe, G. 8 2004 Exponentially-fitted algorithms: fixed or frequency dependent knot points? Zbl 1070.65020 Vanden Berghe, G.; Van Daele, M.; Vande Vyver, H. 8 2004 On the generation of mono-implicit Runge-Kutta-Nyström methods by mono-implicit Runge-Kutta methods. Zbl 0898.65047 De Meyer, H.; Vanden Berghe, G.; Van Hecke, T.; Van Daele, M. 8 1997 Nonscalar extension of shift operator techniques for \(SU(3)\) in an \(O(3)\) basis. I. Theory. Zbl 0495.22015 De Meyer, H. E.; Vanden Berghe, G.; Hughes, J. W. B. 8 1981 Boson realization of the Lie algebra \(F_ 4\) and non-trivial zeros of \(6j\) symbols. Zbl 0537.22019 Van der Jeugt, Joris; Vanden Berghe, G.; De Meyer, H. 8 1983 Shift-operator techniques for the classification of multipole-phonon states. II: Eigenvalues of the quadrupole shift operator \(O^0\). Zbl 0444.22010 De Meyer, H. E.; Vanden Berghe, G. 8 1980 On the spectra of \(\text{SO}(3)\) scalars in the enveloping algebra of \(\text{SU}(3)\). Zbl 0591.22012 De Meyer, Hans; Vanden Berghe, G.; Van der Jeugt, Joris 8 1985 Modified Gregory formulae based on mixed interpolation. Zbl 1306.41010 Bocher, P.; De Meyer, H.; Vanden Berghe, G. 7 1994 Efficient numerical solution of the one-dimensional Schrödinger eigenvalue problem using Magnus integrators. Zbl 1208.65114 Ledoux, Veerle; van Daele, Marnix; Berghe, Guido Vanden 7 2010 Solution of the Schrödinger equation over an infinite integration interval by perturbation methods, revisited. Zbl 1196.81126 Ledoux, V.; Ixaru, L. Gr.; Rizea, M.; Van Daele, M.; Vanden Berghe, G. 7 2006 Solution of the Schrödinger equation by a high order perturbation method based on a linear reference potential. Zbl 1196.81127 Ledoux, V.; Rizea, M.; Ixaru, L.; Vanden Berghe, G.; Van Daele, M. 7 2006 Deferred correction with mono-implicit Runge-Kutta methods for first-order IVPs. Zbl 0945.65079 Van Daele, M.; Van Hecke, T.; Vanden Berghe, G.; De Meyer, H. 7 1999 An entry of Ramanujan on hypergeometric series in his Notebooks. Zbl 1068.33010 Srinivasa Rao, K.; Vanden Berghe, G.; Krattenthaler, C. 7 2005 Nonscalar extension of shift operator techniques for \(SU(3)\) in an \(O(3)\) basis. II. Applications. Zbl 0495.22016 De Meyer, H. E.; Vanden Berghe, G.; Hughes, J. W. B. 7 1981 Shift operator techniques for the classification of multipole-phonon states. III: The quadrupole-phonon eigenstates of \(O^0\). Zbl 0444.22011 De Meyer, H. E.; Vanden Berghe, G. 7 1980 Shift operator techniques for the classification of multipole-phonon states. VI: Properties of nonscalar \(R(3)\) product operators in the \(R(2\lambda +1)\) groups. Zbl 0444.22014 Vanden Berghe, G.; De Meyer, H. E. 7 1980 On Lie algebras built from SO(3) tensor operators. Zbl 0546.22018 Vanden Berghe, G.; de Meyer, H. 7 1984 A finite-element estimate with trigonometric hat functions for Sturm- Liouville eigenvalues. Zbl 0815.65099 vanden Berghe, G.; de Meyer, H. 6 1994 A mono-implicit Runge-Kutta-Nyström modification of the Numerov method. Zbl 0876.65054 Van Hecke, T.; Van Daele, M.; Vanden Berghe, G.; De Meyer, H. 6 1997 Exponential fitting: applications for ODE-solvers. Zbl 1060.65622 Vanden Berghe, G. 6 2004 A general theory of stabilized extended one-step methods for ODEs. Zbl 1001.65518 van Daele, M.; vanden Berghe, G.; de Meyer, H. 6 1996 \(SO(2n+1)\) in an \(SO(2n-3)\times SU(2)\times SU(2)\) basis. II: Detailed study of the symmetric representations of the \(SO(7)\) group. Zbl 0502.22011 Vanden Berghe, G.; de Meyer, H.; de Wilde, P. 6 1982 Nonscalar extension of shift operator techniques for \(\text{SU}(3)\) in an \(\text{O}(3)\) basis. III: Shift operators of second degree in the tensor components. Zbl 0517.22021 Van der Jeugt, Joris; De Meyer, H. E.; Vanden Berghe, G. 6 1983 Shift operator techniques for the classification of multipole-phonon states. IV: Properties of shift operators in the \(G_2\) group. Zbl 0444.22012 Vanden Berghe, G.; De Meyer, H. E. 6 1980 Numerical solution of Volterra equations based on mixed interpolation. Zbl 0805.65142 Bocher, P.; De Meyer, H.; Vanden Berghe, G. 6 1994 Trigonometric polynomial or exponential fitting approach? Zbl 1177.65040 Vanden Berghe, G.; Van Daele, M. 5 2009 A numerical procedure to solve the multichannel Schrödinger eigenvalue problem. Zbl 1196.81108 Ledoux, V.; Van Daele, M.; Vanden Berghe, G. 5 2007 Special issue: Advances in computational and mathematical methods in science and engineering (CMMSE 2009). Selected papers based on the presentations at the conference, Gijón, Spain, June 26–July 1, 2009. Zbl 1213.65013 5 2011 A regularization procedure for \(\sum^ n_{i=1} f_ i (z_ j) x_ i= g(z_ j)\), \((j=1,2,\dots,n)\). Zbl 0841.65021 Ixaru, L. Gr.; de Meyer, H.; Vanden Berghe, G.; Van Daele, M. 5 1996 \(SO(2n+1)\) in an \(SO(2n-3)\times SU(2)\times SU(2)\) basis. I: Reduction of the symmetric representations. Zbl 0498.22021 de Meyer, H.; de Wilde, P.; Vanden Berghe, G. 5 1982 Shift operator techniques for the classification of multipole-phonon states. V: Properties of shift operators in the \(R(7)\) group. Zbl 0444.22013 De Meyer, H. E.; Vanden Berghe, G. 5 1980 Pairs of analytical eigenfunctions for the \(x^ 2+\lambda x^ 2/(1+gx^ 2)\) interaction. Zbl 0679.34016 Vanden Berghe, G.; De Meyer, H. E. 5 1989 Tensor operator realizations of \(E_ 6\) and structural zeros of the \(6j\)-symbol. Zbl 0558.17009 Vanden Berghe, G.; De Meyer, Hans; Van der Jeugt, Joris 5 1984 A variable-step variable-order algorithm for systems of stiff ODEs. Zbl 0871.65076 Van Hecke, T.; Vanden Berghe, G.; Van Daele, M.; De Meyer, H. 4 1997 Five-diagonal finite difference methods based on mixed-type interpolation for a certain fourth-order two-point boundary-value problem. Zbl 0770.65053 Van Daele, M.; Vanden Berghe, G.; De Meyer, H. 4 1992 Numerical solution of Fredholm equations based on mixed interpolation. Zbl 0786.65126 Vanden Berghe, G.; Bocher, P.; De Meyer, H. 4 1993 Accurate high-lying eigenvalues of Schrödinger and Sturm-Liouville problems. Zbl 0959.65500 Vanden Berghe, G.; Van Daele, M.; De Meyer, H. 4 1994 Shift operator approach of the spin-isospin supermultiplet state labelling problem: Eigenvalue determination of the \(\Omega\) and \(\Phi\) labelling operators. Zbl 0538.22014 Van der Jeugt, Joris; De Meyer, H. E.; Vanden Berghe, G. 4 1983 On the symmetric representations of SU(5). Matrix elements of the generators in the SO(3) basis. Zbl 0681.22023 Vanthournout, J.; De Meyer, H.; Vanden Berghe, G. 4 1989 Modified backward differentiation methods of the Adams-type based on exponential interpolation. Zbl 0729.65054 De Meyer, H.; Vanden Berghe, G.; Vanthournout, J. 4 1991 Two-step fourth order methods for linear ODEs of the second order. Zbl 1170.65058 Bulatov, Mikhail V.; Vanden Berghe, Guido 3 2009 A modified Numerov integration method for general second order initial value problems. Zbl 0738.65060 Van Daele, M.; De Meyer, H.; Vanden Berghe, G. 3 1991 Modified Newton-Cotes formulae for numerical quadrature of oscillatory integrals with two independent variable frequencies. Zbl 0765.65025 Van Daele, M.; De Meyer, H.; Vanden Berghe, G. 3 1992 The implementation of parallel Gram-Schmidt orthogonalisation algorithms on a ring of transputers. Zbl 0848.68040 De Meyer, H.; Niyokindi, C.; Vanden Berghe, G. 3 1993 A parallel iterated correction algorithm for the numerical solution of Volterra equations. Zbl 0823.65141 Bocher, P.; De Meyer, H.; Fack, V.; Vanden Berghe, G. 3 1995 Totally symmetric irreducible representations of the group \(\mathrm{SO}(6)\) in the principal \(\mathrm{SO}(3)\) subgroup basis. Zbl 0636.22016 Vanthournout, Jan; Van der Jeugt, Joris; De Meyer, Hans; Vanden Berghe, Guido 3 1987 Exact bound-state solutions of the potential \(V(r)=-Ze^ 2/(r+\beta)\). Zbl 0721.34101 De Meyer, H.; Vanden Berghe, G. 3 1990 Numerical quadrature based on an exponential type of interpolation. Zbl 0728.65018 de Meyer, H.; Vanden Berghe, G.; Vanthournout, J. 3 1991 Exponentially fitted methods applied to fourth-order boundary value problems. Zbl 1225.65075 Hollevoet, D.; Van Daele, M.; Vanden Berghe, G. 12 2011 Symplectic exponentially-fitted four-stage Runge-Kutta methods of the Gauss type. Zbl 1215.65130 Vanden Berghe, Guido; Van Daele, Marnix 9 2011 Special issue: Advances in computational and mathematical methods in science and engineering (CMMSE 2009). Selected papers based on the presentations at the conference, Gijón, Spain, June 26–July 1, 2009. Zbl 1213.65013 5 2011 Symplectic exponentiality-fitted modified Runge-Kutta methods of the Gauss type: Revisited. Zbl 1216.65092 Vanden Berghe, G.; Van Daele, M. 2 2011 Efficient numerical solution of the one-dimensional Schrödinger eigenvalue problem using Magnus integrators. Zbl 1208.65114 Ledoux, Veerle; van Daele, Marnix; Berghe, Guido Vanden 7 2010 The optimal exponentially-fitted Numerov method for solving two-point boundary value problems. Zbl 1167.65406 Hollevoet, D.; Van Daele, M.; Vanden Berghe, G. 58 2009 Exponentially-fitted Obrechkoff methods for second-order differential equations. Zbl 1166.65352 Vanden Berghe, G.; Van Daele, M. 50 2009 Efficient computation of high index Sturm-Liouville eigenvalues for problems in physics. Zbl 1198.65124 Ledoux, V.; Van Daele, M.; Vanden Berghe, Guido 8 2009 Trigonometric polynomial or exponential fitting approach? Zbl 1177.65040 Vanden Berghe, G.; Van Daele, M. 5 2009 Two-step fourth order methods for linear ODEs of the second order. Zbl 1170.65058 Bulatov, Mikhail V.; Vanden Berghe, Guido 3 2009 Eigenvalue problem for a coupled channel Schrödinger equation with application to the description of deformed nuclear systems. Zbl 1165.65046 Ledoux, V.; Rizea, M.; van Daele, M.; vanden Berghe, G.; Silişteanu, I. 2 2009 Finite difference approach for the two-dimensional Schrödinger equation with application to scission-neutron emission. Zbl 1197.81041 Rizea, M.; Ledoux, V.; Van Daele, M.; Vanden Berghe, G.; Carjan, N. 44 2008 ‘Magic is no magic’. The wonderful world of Simon Stevin. Zbl 1133.01011 Devreese, Jozef T.; Vanden Berghe, Guido 1 2008 On the leading error term of exponentially fitted Numerov methods. Zbl 1167.65405 Hollevoet, D.; Van Daele, M.; Vanden Berghe, G. 1 2008 Exponentially-fitted methods applied to fourth-order boundary value problems. Zbl 1167.65410 Van Daele, M.; Hollevoet, D.; Vanden Berghe, G. 1 2008 P-stable exponentially-fitted Obrechkoff methods of arbitrary order for second-order differential equations. Zbl 1134.65043 Van Daele, M.; Vanden Berghe, G. 61 2007 \(P\)-stable Obrechkoff methods of arbitrary order for second-order differential equations. Zbl 1123.65070 Van Daele, Marnix; Vanden Berghe, Guido 49 2007 Exponentially-fitted Numerov methods. Zbl 1110.65071 Vanden Berghe, G.; Van Daele, M. 19 2007 Geometric numerical integration by means of exponentially-fitted methods. Zbl 1116.65125 Van Daele, M.; Vanden Berghe, G. 15 2007 A numerical procedure to solve the multichannel Schrödinger eigenvalue problem. Zbl 1196.81108 Ledoux, V.; Van Daele, M.; Vanden Berghe, G. 5 2007 Exponentially-fitted Störmer/Verlet methods. Zbl 1127.65050 Vanden Berghe, G.; Van Daele, M. 17 2006 Solution of the Schrödinger equation over an infinite integration interval by perturbation methods, revisited. Zbl 1196.81126 Ledoux, V.; Ixaru, L. Gr.; Rizea, M.; Van Daele, M.; Vanden Berghe, G. 7 2006 Solution of the Schrödinger equation by a high order perturbation method based on a linear reference potential. Zbl 1196.81127 Ledoux, V.; Rizea, M.; Ixaru, L.; Vanden Berghe, G.; Van Daele, M. 7 2006 Revisiting a chapter from the notebooks of Ramanujan on hypergeometric series. Zbl 1197.01043 Rao, K. Srinivasa; Vanden Berghe, G. 2 2006 \(CPM\{P,N\}\) methods extended for the solution of coupled channel Schrödinger equations. Zbl 1196.65115 Ledoux, V.; Van Daele, M.; Vanden Berghe, G. 2 2006 MATSLISE: a MATLAB package for the numerical solution of Sturm-Liouville and Schrödinger equations. Zbl 1136.65327 Ledoux, Veerle; Van Daele, Marnix; Vanden Berghe, Guido 42 2005 Exponentially fitted quadrature rules of Gauss type for oscillatory integrands. Zbl 1069.65022 Van Daele, M.; Vanden Berghe, G.; Vande Vyver, H. 9 2005 An entry of Ramanujan on hypergeometric series in his Notebooks. Zbl 1068.33010 Srinivasa Rao, K.; Vanden Berghe, G.; Krattenthaler, C. 7 2005 Exponential fittings: general approach and applications for ODE-solvers. Zbl 1074.65073 Vanden Berghe, Guido 2 2005 Exponentially-fitted geometric numerical integration. Zbl 1088.65557 Vanden Berghe, G.; Van Daele, M. 1 2005 CP methods and the evaluation of negative energy Coulomb Whittaker functions. Zbl 1074.65077 Ledoux, V.; Van Daele, M.; Vanden Berghe, G. 1 2005 Exponential fitting. With CD-ROM. Zbl 1105.65082 Ixaru, Liviu Gr.; Vanden Berghe, Guido 110 2004 Approximate solution of singular integral equations. Zbl 1061.65141 Chakrabarti, A.; Vanden Berghe, G. 15 2004 CP methods of higher order for Sturm-Liouville and Schrödinger equations. Zbl 1196.65131 Ledoux, V.; Van Daele, M.; Vanden Berghe, Guido 11 2004 Extended one-step methods: An exponential fitting approach. Zbl 1063.65063 Van Daele, M.; Vanden Berghe, G. 8 2004 Exponentially-fitted algorithms: fixed or frequency dependent knot points? Zbl 1070.65020 Vanden Berghe, G.; Van Daele, M.; Vande Vyver, H. 8 2004 Exponential fitting: applications for ODE-solvers. Zbl 1060.65622 Vanden Berghe, G. 6 2004 Exponentially fitted variable two-step BDF algorithm for first order ODEs. Zbl 1196.65110 Ixaru, L. Gr.; Vanden Berghe, Guido; De Meyer, Hans 64 2003 Exponential fitted Runge-Kutta methods of collocation type: Fixed or variable knot points? Zbl 1031.65084 Vanden Berghe, G.; Van Daele, M.; Vande Vyver, H. 31 2003 A special identity between three \(_{2} F_{1}(a,b;c;4)\) hypergeometric series. Zbl 1031.33003 Vanden Berghe, G.; De Meyer, H. 1 2003 Frequency evaluation in exponential fitting multistep algorithms for ODEs. Zbl 0996.65075 Ixaru, L. Gr.; Vanden Berghe, G.; De Meyer, H. 103 2002 Weights of the exponential fitting multistep algorithms for first-order ODEs. Zbl 0991.65061 Ixaru, L. Gr.; Rizea, M.; Vanden Berghe, G.; De Meyer, H. 60 2001 Frequency determination and step-length control for exponentially-fitted Runge-Kutta methods. Zbl 0991.65062 Vanden Berghe, G.; Ixaru, L. Gr.; De Meyer, H. 35 2001 Optimal implicit exponentially-fitted Runge-Kutta methods. Zbl 0990.65080 Vanden Berghe, G.; Ixaru, L. Gr.; Van Daele, M. 29 2001 Exponentially fitted Runge-Kutta methods. Zbl 0999.65065 Vanden Berghe, G.; De Meyer, H.; Van Daele, M.; Van Hecke, T. 69 2000 Exponentially-fitted explicit Runge-Kutta methods. Zbl 0948.65066 Vanden Berghe, G.; De Meyer, H.; Van Daele, M.; Van Hecke, T. 95 1999 SLCPM12 – a program for solving regular Sturm-Liouville problems. Zbl 1008.34016 Ixaru, L. Gr.; De Meyer, H.; Vanden Berghe, G. 14 1999 Deferred correction with mono-implicit Runge-Kutta methods for first-order IVPs. Zbl 0945.65079 Van Daele, M.; Van Hecke, T.; Vanden Berghe, G.; De Meyer, H. 7 1999 Exponential-fitted four-step methods for \(y''=f(x,y)\). Zbl 0894.65032 Van Daele, M.; Vanden Berghe, G.; De Meyer, H.; Ixaru, L. Gr. 47 1998 CP methods for the Schrödinger equation revisited. Zbl 0909.65045 Ixaru, L. Gr.; De Meyer, H.; Vanden Berghe, G. 16 1998 On a class of \(P\)-stable mono-implicit Runge-Kutta-Nyström methods. Zbl 0937.65085 Van Daele, M.; De Meyer, H.; Van Hecke, T.; Vanden Berghe, G. 9 1998 Special functions and differential equations. Proceedings of a workshop, WSSF ’97, Madras, India, January 13–24, 1997. Zbl 0914.00063 2 1998 Four-step exponential-fitted methods for nonlinear physical problems. Zbl 0927.65100 Ixaru, L. Gr.; Vanden Berghe, G.; De Meyer, H.; Van Daele, M. 52 1997 EXPFIT4 – a FORTRAN program for the numerical solution of systems of nonlinear second-order initial-value problems. Zbl 0927.65099 Ixaru, L. Gr.; De Meyer, H.; Vanden Berghe, G.; Van Daele, M. 49 1997 On the generation of mono-implicit Runge-Kutta-Nyström methods by mono-implicit Runge-Kutta methods. Zbl 0898.65047 De Meyer, H.; Vanden Berghe, G.; Van Hecke, T.; Van Daele, M. 8 1997 A mono-implicit Runge-Kutta-Nyström modification of the Numerov method. Zbl 0876.65054 Van Hecke, T.; Van Daele, M.; Vanden Berghe, G.; De Meyer, H. 6 1997 A variable-step variable-order algorithm for systems of stiff ODEs. Zbl 0871.65076 Van Hecke, T.; Vanden Berghe, G.; Van Daele, M.; De Meyer, H. 4 1997 A general theory of stabilized extended one-step methods for ODEs. Zbl 1001.65518 van Daele, M.; vanden Berghe, G.; de Meyer, H. 6 1996 A regularization procedure for \(\sum^ n_{i=1} f_ i (z_ j) x_ i= g(z_ j)\), \((j=1,2,\dots,n)\). Zbl 0841.65021 Ixaru, L. Gr.; de Meyer, H.; Vanden Berghe, G.; Van Daele, M. 5 1996 Multistride \(L\)-stable fourth-order methods for the numerical solution of ODEs. Zbl 0866.65052 De Meyer, H.; Van Hecke, T.; Vanden Berghe, G.; Van Daele, M. 2 1996 A parallel fifth-order algorithm for the numerical solution of Volterra equations. Zbl 0855.65139 De Meyer, H.; Bocher, P.; Fack, V.; Vanden Berghe, G. 2 1996 Properties and implementation of \(r\)-Adams methods based on mixed-type interpolation. Zbl 0837.65079 Van Daele, M.; Vanden Berghe, G.; De Meyer, H. 46 1995 A modified difference scheme for periodic and semiperiodic Sturm- Liouville problems. Zbl 0834.65075 Vanden Berghe, G.; Van Daele, M.; De Meyer, H. 9 1995 A parallel iterated correction algorithm for the numerical solution of Volterra equations. Zbl 0823.65141 Bocher, P.; De Meyer, H.; Fack, V.; Vanden Berghe, G. 3 1995 Exact solutions for radial Schrödinger equations. Zbl 0835.34002 Vanden Berghe, G.; De Meyer, H.; van Daele, M. 2 1995 A smooth approximation for the solution of a fourth-order boundary value problem based on nonpolynomial splines. Zbl 0810.65079 van Daele, M.; vanden Berghe, G.; de Meyer, H. 22 1994 On Gregory-and modified Gregory-type corrections to Newton-Cotes quadrature. Zbl 0808.41020 Bocher, P.; de Meyer, H.; vanden Berghe, G. 8 1994 Modified Gregory formulae based on mixed interpolation. Zbl 1306.41010 Bocher, P.; De Meyer, H.; Vanden Berghe, G. 7 1994 A finite-element estimate with trigonometric hat functions for Sturm- Liouville eigenvalues. Zbl 0815.65099 vanden Berghe, G.; de Meyer, H. 6 1994 Numerical solution of Volterra equations based on mixed interpolation. Zbl 0805.65142 Bocher, P.; De Meyer, H.; Vanden Berghe, G. 6 1994 Accurate high-lying eigenvalues of Schrödinger and Sturm-Liouville problems. Zbl 0959.65500 Vanden Berghe, G.; Van Daele, M.; De Meyer, H. 4 1994 Structural zeros of Racah coefficients and exceptional Lie algebras. Zbl 0818.17003 Vanden Berghe, G. 2 1994 Numerical integration based on mixed-typ interpolation for a fourth-order boundary-value problem. Zbl 0802.65092 Van Daele, M.; Vanden Berghe, G.; De Meyer, H. 1 1994 Numerical solution of Fredholm equations based on mixed interpolation. Zbl 0786.65126 Vanden Berghe, G.; Bocher, P.; De Meyer, H. 4 1993 The implementation of parallel Gram-Schmidt orthogonalisation algorithms on a ring of transputers. Zbl 0848.68040 De Meyer, H.; Niyokindi, C.; Vanden Berghe, G. 3 1993 On the implementation of parallel iterated Runge-Kutta methods on a transputer network. Zbl 0786.65059 De Meyer, H.; Van Daele, M.; Vanden Berghe, G. 1 1993 A parallel approach to the modified Numerov-like eigenvalue determination for Sturm-Liouville problems. Zbl 0773.65066 Vanden Berghe, G.; De Meyer, H.; Van Daele, M. 9 1992 Multistep methods for ordinary differential equations based on algebraic and first order trigonometric polynomials. Zbl 0768.65044 Vanthournout, J.; De Meyer, H.; Vanden Berghe, G. 8 1992 Five-diagonal finite difference methods based on mixed-type interpolation for a certain fourth-order two-point boundary-value problem. Zbl 0770.65053 Van Daele, M.; Vanden Berghe, G.; De Meyer, H. 4 1992 Modified Newton-Cotes formulae for numerical quadrature of oscillatory integrals with two independent variable frequencies. Zbl 0765.65025 Van Daele, M.; De Meyer, H.; Vanden Berghe, G. 3 1992 On the algebra of coupled SO(3) tensors. Zbl 0749.17005 Srinivasa Rao, K.; Van der Jeugt, Joris; Vanden Berghe, G. 2 1992 A five-diagonal finite-difference method based on mixed-type interpolation for computing eigenvalues of fourth-order two-point boundary-value problems. Zbl 0759.65055 Vanden Berghe, G.; Van Daele, M.; De Meyer, H. 2 1992 Accurate computation of higher Sturm-Liouville eigenvalues. Zbl 0716.65079 Vanden Berghe, G.; De Meyer, H. 14 1991 On a correction of Numerov-like eigenvalue approximations for Sturm- Liouville problems. Zbl 0753.65071 Vanden Berghe, G.; de Meyer, H. 11 1991 Modified backward differentiation methods of the Adams-type based on exponential interpolation. Zbl 0729.65054 De Meyer, H.; Vanden Berghe, G.; Vanthournout, J. 4 1991 A modified Numerov integration method for general second order initial value problems. Zbl 0738.65060 Van Daele, M.; De Meyer, H.; Vanden Berghe, G. 3 1991 Numerical quadrature based on an exponential type of interpolation. Zbl 0728.65018 de Meyer, H.; Vanden Berghe, G.; Vanthournout, J. 3 1991 On a new type of mixed interpolation. Zbl 0693.41003 De Meyer, H.; Vanthournout, J.; Vanden Berghe, G. 44 1990 On the error estimation for a mixed type of interpolation. Zbl 0725.41002 De Meyer, H.; Vanthournout, J.; Van den Berghe, G. 32 1990 A modified Numerov integration method for second order periodic initial- value problems. Zbl 0752.65059 Vanden Berghe, G.; De Meyer, H.; Vanthournout, J. 23 1990 On a class of modified Newton-Cotes quadrature formulae based upon mixed- type interpolation. Zbl 0729.41032 Vanden Berghe, G.; De Meyer, H.; Vanthournout, J. 21 1990 Families of backward differentiation methods based on a new type of mixed interpolation. Zbl 0752.65060 Vanthournout, Jan; Vanden Berghe, Guido; De Meyer, Hans 18 1990 A modified Numerov method for higher Sturm-Liouville eigenvalues. Zbl 0726.65100 Vanden Berghe, G.; de Meyer, H. 14 1990 Exact bound-state solutions of the potential \(V(r)=-Ze^ 2/(r+\beta)\). Zbl 0721.34101 De Meyer, H.; Vanden Berghe, G. 3 1990 Numerical methods for solving radial Schrödinger equations. Zbl 0694.65033 Vanden Berghe, G.; Fack, V.; De Meyer, H. E. 19 1989 Pairs of analytical eigenfunctions for the \(x^ 2+\lambda x^ 2/(1+gx^ 2)\) interaction. Zbl 0679.34016 Vanden Berghe, G.; De Meyer, H. E. 5 1989 On the symmetric representations of SU(5). Matrix elements of the generators in the SO(3) basis. Zbl 0681.22023 Vanthournout, J.; De Meyer, H.; Vanden Berghe, G. 4 1989 On the symmetric representations of \(\text{SU}(5)\). Matrix elements of the generators in the subgroup bases \(\text{SU}(2)\times\text{SU}(2)\times\text{U}(1)\) and \(\text{SU}(2)\times\text{SU}(2)\). Zbl 0653.22013 Vanthournout, Jan; De Meyer, Hans; Vanden Berghe, Guido 1 1988 (Extended) Numerov method for computing eigenvalues of specific Schrödinger equations. Zbl 0626.65079 Fack, V.; Vanden Berghe, G. 13 1987 Some finite difference methods for computing eigenvalues and eigenvectors of special two-point boundary value problems. Zbl 0635.65101 Fack, V.; Vanden Berghe, G.; De Meyer, H. E. 11 1987 ...and 27 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 580 Authors 107 Simos, Theodore E. 86 Vanden Berghe, Guido 65 De Meyer, Hans E. 49 Van Daele, Marnix 36 Paternoster, Beatrice 28 Fang, Yonglei 27 You, Xiong 24 Ixaru, Liviu Gr. 20 D’Ambrosio, Raffaele 20 Wu, Xinyuan 18 Lin, Chialiang 18 Van der Jeugt, Joris 17 Franco, J. Méndez 17 Van de Vyver, Hans 17 Vigo-Aguiar, Jesus 14 Conte, Dajana 14 Rández, Luis 12 Jator, Samuel N. 11 Anastassi, Zacharias A. 11 Kalogiratou, Zacharoula 11 Ramos, Higinio 10 Ledoux, Veerle 10 Martín-Vaquero, Jesús 10 Van Hecke, Tanja 9 Cardone, Angelamaria 9 Medvedeva, Marina A. 9 Vanthournout, Jan 8 Li, Jiyong 8 Montijano, Juan Ignacio 7 Bocher, Philippe 7 Calvo, Manuel 7 Chen, Zhaoxia 7 Ghelardoni, Paolo 7 Li, Qinghong 7 Magherini, Cecilia 7 Medvedev, Maxim A. 7 Yang, Yanping 6 Kim, Kyung Joong 6 Kravchenko, Vladislav V. 6 Okunuga, Solomon A. 6 Vlachos, Dimitrios 6 Wang, Bin 6 Zhao, Longbin 5 Aceto, Lidia 5 Chakrabarti, Aloknath 5 Chen, Bingzhen 5 Ehigie, Julius Osato 5 Esposito, Elena 5 Hamsapriye 5 Ismail, Fudziah Bt. 5 Jalilian, Reza 5 Ming, Qinghe 5 Ngwane, Fidele F. 5 Pagano, Giovanni 5 Tsitouras, Charalampos 5 Witwit, M. R. M. 5 Zahra, Waheed K. 5 Zhai, Wenjuan 5 Zheng, Juan 4 Abdulganiy, Ridwanulahi Iyanda 4 Akram, Ghazala 4 Brugnano, Luigi 4 Dewilde, Patrick M. 4 El-Daou, Mohamed K. 4 Fack, Veerle 4 Hughes, J. W. B. 4 Khalsaraei, Mohammad Mehdizadeh 4 Liu, Shiwei 4 Monovasilis, Theodoros 4 Ozawa, Kazufumi 4 Shi, Wei 4 Sun, Bin 4 Torba, Sergii M. 4 Yang, Hongli 4 Zhang, Ruqiang 3 Akinfenwa, Olusheye Aremu Akin 3 Amodio, Pierluigi 3 Baeyens, Toon 3 Çelik, İbrahim 3 Cong, Nguyen Huu 3 Deng, Shuo 3 El-Danaf, Talaat S. Aly 3 Erdoğan, Utku 3 García-Alonso, Fernando 3 Garcia-Rubio, Raquel 3 García, Amelia 3 Hollevoet, D. 3 Huang, Chengming 3 Iavernaro, Felice 3 Konguetsof, Avrilia 3 Louck, James D. 3 Martín, Pablo 3 Moccaldi, Martina 3 Ramadan, Mohamed Abdel-Latif 3 Reyes, José Antonio 3 Santomauro, Giuseppe 3 Senu, Norazak 3 Siddiqi, Shahid Saeed 3 Sidje, Roger B. 3 Siraj-ul-Islam ...and 480 more Authors all top 5 Cited in 119 Serials 132 Journal of Computational and Applied Mathematics 85 Journal of Mathematical Chemistry 67 Applied Mathematics and Computation 48 Journal of Mathematical Physics 47 Computer Physics Communications 39 Applied Numerical Mathematics 27 Numerical Algorithms 26 International Journal of Computer Mathematics 18 Computers & Mathematics with Applications 10 Journal of Computational Physics 8 Physics Letters. 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Series B 1 Journal of Applied Mathematics and Computing ...and 19 more Serials all top 5 Cited in 44 Fields 562 Numerical analysis (65-XX) 273 Ordinary differential equations (34-XX) 136 Quantum theory (81-XX) 53 Partial differential equations (35-XX) 39 Topological groups, Lie groups (22-XX) 35 Integral equations (45-XX) 30 Approximations and expansions (41-XX) 29 Dynamical systems and ergodic theory (37-XX) 22 Special functions (33-XX) 17 Nonassociative rings and algebras (17-XX) 11 Mechanics of particles and systems (70-XX) 11 Biology and other natural sciences (92-XX) 10 Operator theory (47-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 6 Mechanics of deformable solids (74-XX) 6 Fluid mechanics (76-XX) 5 General and overarching topics; collections (00-XX) 5 Number theory (11-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 4 Algebraic geometry (14-XX) 4 Group theory and generalizations (20-XX) 4 Real functions (26-XX) 4 Optics, electromagnetic theory (78-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Difference and functional equations (39-XX) 3 Functional analysis (46-XX) 3 Statistics (62-XX) 3 Computer science (68-XX) 2 History and biography (01-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Geophysics (86-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Sequences, series, summability (40-XX) 1 Integral transforms, operational calculus (44-XX) 1 Geometry (51-XX) 1 Probability theory and stochastic processes (60-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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