Edit Profile (opens in new tab) Rach, Randolph C. Co-Author Distance Author ID: rach.randolph-c Published as: Rach, R.; Rach, Randolph; Rach, Randolph C.; Rach, R. C. more...less Documents Indexed: 113 Publications since 1983 Co-Authors: 32 Co-Authors with 105 Joint Publications 511 Co-Co-Authors all top 5 Co-Authors 7 single-authored 55 Adomian, George 26 Duan, Junsheng 21 Wazwaz, Abdul-Majid Abdul-Rahman 17 Bougoffa, Lazhar 6 Meyers, Ronald E. 4 Chaolu, Temuer 4 Mennouni, Abdelaziz 3 Elrod, M. 2 Mziou, Samy 2 Wang, Zhong 1 Abadyan, Mohamadreza 1 Abdelwahid, Fawzi 1 Abolghasemi, Hossein 1 Adesanya, Samuel Olumide 1 Al-Haqbani, Manal 1 Aly, Emad H. 1 Didgar, Mohsen 1 Ebaid, Abdelhalim 1 El Manouni, Said 1 Falade, John A. 1 Farrokhabadi, Amin 1 Fatoorehchi, Hooman 1 Hu, Dichen 1 Lin, Shi-Ming 1 Lu, Lei 1 Mokhtari, Javad 1 Sarafyan, Diran 1 Sibul, Leon H. 1 Vahidi, A. R. 1 Wen, Ying 1 Yun, Yinshan 1 Zarghami, Reza all top 5 Serials 26 Journal of Mathematical Analysis and Applications 15 Applied Mathematics and Computation 11 Computers & Mathematics with Applications 11 Applied Mathematics Letters 9 Kybernetes 3 Mathematical Methods in the Applied Sciences 3 Journal of Computational and Applied Mathematics 3 International Journal for Computational Methods in Engineering Science and Mechanics 2 International Journal of Computer Mathematics 2 Journal of Mathematical Chemistry 2 CMES. Computer Modeling in Engineering & Sciences 2 Mathematical Modelling and Analysis 2 Journal of Applied Mathematics and Computing 2 MATCH - Communications in Mathematical and in Computer Chemistry 2 Scientia. Series A: Mathematical Sciences. New Series 1 International Journal of Modern Physics B 1 Indian Journal of Pure & Applied Mathematics 1 Journal of Mathematical and Physical Sciences 1 Chaos, Solitons and Fractals 1 Mathematics and Computers in Simulation 1 Mathematical Modelling 1 Mathematical and Computer Modelling 1 Journal of Natural & Physical Sciences 1 Applied Mathematical Modelling 1 International Journal of Numerical Methods for Heat & Fluid Flow 1 Theoretical and Applied Mechanics 1 Advances in Difference Equations 1 International Journal of Biomathematics 1 International Journal of Dynamical Systems and Differential Equations 1 Journal of Algorithms & Computational Technology 1 Journal of Applied Analysis and Computation 1 Nonlinear Analysis. Theory, Methods & Applications all top 5 Fields 52 Ordinary differential equations (34-XX) 50 Numerical analysis (65-XX) 22 Partial differential equations (35-XX) 17 Probability theory and stochastic processes (60-XX) 7 Integral equations (45-XX) 7 Biology and other natural sciences (92-XX) 6 Approximations and expansions (41-XX) 6 Systems theory; control (93-XX) 3 Sequences, series, summability (40-XX) 3 Mechanics of deformable solids (74-XX) 2 Functions of a complex variable (30-XX) 2 Operator theory (47-XX) 2 Mechanics of particles and systems (70-XX) 2 Fluid mechanics (76-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Quantum theory (81-XX) 1 History and biography (01-XX) 1 Real functions (26-XX) 1 Special functions (33-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Statistical mechanics, structure of matter (82-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 101 Publications have been cited 1,814 times in 912 Documents Cited by ▼ Year ▼ Inversion of nonlinear stochastic operators. Zbl 0504.60066 Adomian, G.; Rach, R. 159 1983 Nonlinear stochastic differential delay equations. Zbl 0504.60067 Adomian, G.; Rach, R. 106 1983 Noise terms in decomposition solution series. Zbl 0777.35018 Adomian, G.; Rach, R. 87 1992 A convenient computational form for the Adomian polynomials. Zbl 0552.60061 Rach, Randolph 86 1984 Analytic solution of nonlinear boundary-value problems in serveral dimensions by decomposition. Zbl 0796.35017 Adomian, G.; Rach, R. 67 1993 A new definition of the Adomian polynomials. Zbl 1176.33023 Rach, Randolph C. 60 2008 A new modification of the Adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations. Zbl 1521.65071 Duan, Jun-Sheng; Rach, Randolph 59 2011 On the solution of algebraic equations by the decomposition method. Zbl 0552.60060 Adomian, G.; Rach, R. 58 1985 Equality of partial solutions in the decomposition method for linear or nonlinear partial differential equations. Zbl 0702.35058 Adomian, G.; Rach, R. 54 1990 Solving coupled Lane-Emden boundary value problems in catalytic diffusion reactions by the Adomian decomposition method. Zbl 1311.92222 Rach, Randolph; Duan, Jun-Sheng; Wazwaz, Abdul-Majid 51 2014 Modified decomposition solution of linear and nonlinear boundary-value problems. Zbl 0810.34015 Adomian, G.; Rach, R. 45 1994 Adomian decomposition method for solving the Volterra integral form of the Lane-Emden equations with initial values and boundary conditions. Zbl 1282.65082 Wazwaz, Abdul-Majid; Rach, Randolph; Duan, Jun-Sheng 41 2013 Modified Adomian polynomials. Zbl 0874.65051 Adomian, G.; Rach, R. 40 1996 On the Adomian (decomposition) method and comparisons with Picard’s method. Zbl 0645.60067 Rach, R. 37 1987 A modified decomposition. Zbl 0756.35013 Rach, R.; Adomian, G.; Meyers, R. E. 36 1992 Transformation of series. Zbl 0742.40004 Adomian, G.; Rach, R. 34 1991 A new modified Adomian decomposition method and its multistage form for solving nonlinear boundary value problems with Robin boundary conditions. Zbl 1426.65122 Duan, Jun-Sheng; Rach, Randolph; Wazwaz, Abdul-Majid; Chaolu, Temuer; Wang, Zhong 34 2013 An efficient methodology for the physical sciences. Zbl 0744.65039 Adomian, G.; Rach, R. C.; Meyers, R. E. 28 1991 Comparison of the Adomian decomposition method and the variational iteration method for solving the Lane-Emden equations of the first and second kinds. Zbl 1511.65079 Wazwaz, Abdul-Majid; Rach, Randolph 25 2011 The Adomian decomposition method with convergence acceleration techniques for nonlinear fractional differential equations. Zbl 1348.34010 Duan, Jun-Sheng; Chaolu, Temuer; Rach, Randolph; Lu, Lei 23 2013 A study on the systems of the Volterra integral forms of the Lane-Emden equations by the Adomian decomposition method. Zbl 1302.34024 Wazwaz, Abdul-Majid; Rach, Randolph; Duan, Jun-Sheng 23 2014 Polynomial nonlinearities in differential equations. Zbl 0606.34009 Adomian, G.; Rach, R. 22 1985 Generalization of Adomian polynomials to functions of several variables. Zbl 0765.34005 Adomian, G.; Rach, R. 21 1992 Solutions of the initial value problem for nonlinear fractional ordinary differential equations by the rach-Adomian-meyers modified decomposition method. Zbl 1245.65087 Duan, Jun-Sheng; Chaolu, Temuer; Rach, Randolph 19 2012 A bibliography of the theory and applications of the Adomian decomposition method, 1961–2011. Zbl 1511.65112 Rach, Randolph 19 2012 Steady-state concentrations of carbon dioxide absorbed into phenyl glycidyl ether solutions by the Adomian decomposition method. Zbl 1323.34024 Duan, Jun-Sheng; Rach, Randolph; Wazwaz, Abdul-Majid 18 2015 Nonlinear transformation of series. II. Zbl 0768.40001 Adomian, G.; Rach, R. 17 1992 On composite nonlinearities and the decomposition method. Zbl 0617.65046 Adomian, G.; Rach, R. 17 1986 New higher-order numerical one-step methods based on the Adomian and the modified decomposition methods. Zbl 1478.65071 Duan, Jun-Sheng; Rach, Randolph 17 2011 Numerical integration, analytic continuation, and decomposition. Zbl 0905.65079 Adomian, G.; Rach, R. C.; Meyers, R. E. 16 1997 A new algorithm for matching boundary conditions in decomposition solutions. Zbl 0780.65045 Adomian, G.; Rach, R. 16 1993 Near-field and far-field approximations by the Adomian and asymptotic decomposition methods. Zbl 1209.65071 Rach, Randolph; Duan, Jun-Sheng 14 2011 The noisy convergence phenomena in decomposition method solutions. Zbl 0616.65084 Adomian, G.; Rach, R. 14 1986 A new approach to boundary value equations and application to a generalization of Airy’s equation. Zbl 0678.65057 Adomian, G.; Elrod, M.; Rach, R. 13 1989 Algebraic computation and the decomposition method. Zbl 0604.60064 Adomian, G.; Rach, R. 13 1986 Numerical algorithms and decomposition. Zbl 0728.65068 Adomian, G.; Rach, R.; Meyers, Ronald E. 13 1991 Differential equations with singular coefficients. Zbl 0748.65066 Rach, R.; Baghdasarian, A.; Adomian, G. 12 1992 On the solution of partial differential equations with specified boundary conditions. Zbl 0678.65084 Adomian, G.; Rach, R.; Elrod, M. 12 1989 On linear and nonlinear integro-differential equations. Zbl 0601.45009 Adomian, G.; Rach, R. 12 1986 A convenient technique for solving linear and nonlinear Abel integral equations by the Adomian decomposition method. Zbl 1252.65207 Bougoffa, Lazhar; Rach, Randolph C.; Mennouni, Abdelaziz 12 2011 Solving nonlocal initial-boundary value problems for linear and nonlinear parabolic and hyperbolic partial differential equations by the Adomian decomposition method. Zbl 1334.65177 Bougoffa, Lazhar; Rach, Randolph C. 12 2013 Chaos control in the cerium-catalyzed Belousov-Zhabotinsky reaction using recurrence quantification analysis measures. Zbl 1352.93053 Fatoorehchi, Hooman; Zarghami, Reza; Abolghasemi, Hossein; Rach, Randolph 12 2015 Modified decomposition solution of nonlinear partial differential equations. Zbl 0794.35023 Adomian, G.; Rach, R. 11 1992 A further consideration of partial solutions in the decomposition method. Zbl 0756.35012 Adomian, G.; Rach, R. 11 1992 On the solution of equations containing radicals by the decomposition method. Zbl 0579.60060 Adomian, G.; Rach, R.; Sarafyan, D. 11 1985 Solving Cauchy integral equations of the first kind by the Adomian decomposition method. Zbl 1416.65529 Bougoffa, Lazhar; Mennouni, Abdelaziz; Rach, Randolph C. 11 2013 Inhomogeneous nonlinear partial differential equations with variable coefficients. Zbl 0758.35023 Adomian, G.; Rach, R. 10 1992 Higher order numeric solutions of the Lane-Emden-type equations derived from the multi-stage modified Adomian decomposition method. Zbl 1366.65069 Duan, Jun-Sheng; Rach, Randolph; Wazwaz, Abdul-Majid 10 2017 A nonlinear differential delay equation. Zbl 0504.60068 Adomian, G.; Rach, R. 10 1983 An approximate method for solving a class of weakly-singular Volterra integro-differential equations. Zbl 1219.65159 Bougoffa, Lazhar; Rach, Randolph C.; Mennouni, Abdelaziz 10 2011 Coupled differential equations and coupled boundary conditions. Zbl 0579.60057 Adomian, G.; Rach, R. 9 1985 Application of the decomposition method to inversion of matrices. Zbl 0598.65011 Adomian, G.; Rach, R. 9 1985 Advances in the Adomian decomposition method for solving two-point nonlinear boundary value problems with Neumann boundary conditions. Zbl 1247.65097 Aly, Emad H.; Ebaid, Abdelhalim; Rach, Randolph 9 2012 A reliable modification of the Adomian decomposition method for higher-order nonlinear differential equations. Zbl 1511.65076 Rach, Randolph; Wazwaz, Abdul-Majid; Duan, Jun-Sheng 9 2013 On solutions of boundary value problem for fourth-order beam equations. Zbl 1488.34116 Bougoffa, Lazhar; Rach, Randolph; Wazwaz, Abdul-Majid 9 2016 On the Adomian decomposition method for solving the Stefan problem. Zbl 1356.80034 Bougoffa, Lazhar; Rach, Randolph; Wazwaz, Abdul-Majid; Duan, Jun-Sheng 8 2015 Algebraic equations with exponential terms. Zbl 0579.60058 Adomian, G.; Rach, R. 7 1985 Nonlinear differential equations with negative power nonlinearities. Zbl 0579.60059 Adomian, G.; Rach, R. 7 1985 Solving nonlinear differential equations with decimal power nonlinearities. Zbl 0591.60052 Adomian, G.; Rach, R. 7 1986 Coupled nonlinear stochastic differential equations. Zbl 0517.60064 Adomian, G.; Sibul, L. H.; Rach, R. 7 1983 Two reliable methods for solving the Volterra integral equation with a weakly singular kernel. Zbl 1416.65557 Wazwaz, Abdul-Majid; Rach, Randolph 7 2016 Multiple decompositions for computational convenience. Zbl 0707.34008 Rach, R.; Adomian, G. 7 1990 Solving new fourth-order Emden-Fowler-type equations by the Adomian decomposition method. Zbl 1549.34055 Wazwaz, Abdul-Majid; Rach, Randolph; Duan, Jun-Sheng 7 2015 Solving the Lane-Emden-Fowler type equations of higher orders by the Adomian decomposition method. Zbl 1356.65214 Wazwaz, Abdul-Majid; Rach, Randolph; Bougoffa, Lazhar; Duan, Jun-Sheng 7 2014 On the solution of nonlinear differential equations with convolution product nonlinearities. Zbl 0588.34004 Adomian, G.; Rach, R. 6 1986 Higher-order numeric Wazwaz-El-Sayed modified Adomian decomposition algorithms. Zbl 1247.65109 Duan, Jun-Sheng; Rach, Randolph 6 2012 Variational iteration method for solving oxygen and carbon substrate concentrations in microbial floc particles. Zbl 1466.92118 Wazwaz, Abdul-Majid; Rach, Randolph; Duan, Jun-Sheng 6 2016 Solution of nonlinear partial differential equations in one, two, three, and four dimensions. Zbl 0834.65058 Adomian, G.; Rach, R. 5 1993 The decomposition method applied to stiff systems. Zbl 0645.65040 Adomian, G.; Rach, R.; Elrod, M. 5 1988 A reliable analysis of oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics. Zbl 1330.92037 Rach, Randolph; Wazwaz, Abdul-Majid; Duan, Jun-Sheng 5 2014 A new computational approach for inversion of very large matrices. Zbl 0613.65023 Adomian, G.; Rach, R. 5 1986 On the effective region of convergence of the decomposition series solution. Zbl 1280.65083 Duan, Jun-Sheng; Rach, Randolph; Wang, Zhong 5 2013 A convenient technique for solving integral equations of the first kind by the Adomian decomposition method. Zbl 1511.65145 Bougoffa, Lazhar; Al-Haqbani, Manal; Rach, Randolph C. 5 2012 Oxygen and carbon substrate concentrations in microbial floc particles by the Adomian decomposition method. Zbl 1468.92030 Duan, Jun-Sheng; Rach, Randolph; Wazwaz, Abdul-Majid 5 2015 Solution of nonlinear ordinary and partial differential equations of physics. Zbl 0792.34006 Adomian, G.; Rach, R. 4 1991 A new modified Adomian decomposition method for higher-order nonlinear dynamical systems. Zbl 1356.65207 Duan, Jun-Sheng; Rach, Randolph; Wazwaz, Abdul-Majid 4 2013 Solving nonlocal initial-boundary value problems for the Lotka-von Foerster model. Zbl 1334.65178 Bougoffa, Lazhar; Rach, Randolph C.; Wazwaz, Abdul-Majid 4 2013 Smooth polynomial expansions of piecewise-differentiable functions. Zbl 0721.41043 Rach, R.; Adomian, G. 4 1989 Modeling the influence of the Casimir force on the pull-in instability of nanowire-fabricated nanotweezers. Zbl 1308.81158 Farrokhabadi, Amin; Mokhtari, Javad; Rach, Randolph; Abadyan, Mohamadreza 4 2015 The Volterra integral form of the Lane-Emden equation: new derivations and solution by the Adomian decomposition method. Zbl 1322.34022 Rach, Randolph; Wazwaz, Abdul-Majid; Duan, Jun-Sheng 4 2015 Analytic parametrization and the decomposition method. Zbl 0754.60066 Adomian, G.; Rach, R. 3 1989 Nonlinear plasma response. Zbl 0575.60063 Adomian, G.; Rach, R. 3 1985 An improved approximate analytic solution for Riccati equations over extended intervals. Zbl 1310.34022 Vahidi, A. R.; Didgar, M.; Rach, R. C. 3 2014 Anharmonic oscillator systems. Zbl 0517.70026 Adomian, G.; Rach, R. 3 1983 A convergence analysis of the Adomian decomposition method for an abstract Cauchy problem of a system of first-order nonlinear differential equations. Zbl 1321.65108 Bougoffa, Lazhar; Rach, Randolph C.; El-Manouni, Said 3 2013 Analytic approximation of the blow-up time for nonlinear differential equations by the ADM-Padé technique. Zbl 1283.34031 Duan, Jun-Sheng; Rach, Randolph; Lin, Shi-Ming 3 2013 Simulation of the eigenvalue problem for tapered rotating beams by the modified decomposition method. Zbl 1541.74051 Duan, Jun-Sheng; Rach, Randolph; Wazwaz, Abdul-Majid 3 2022 Exact and approximate analytic solutions of the Jeffery-Hamel flow problem by the Duan-Rach modified Adomian decomposition method. Zbl 1488.65180 Bougoffa, Lazhar; Mziou, Samy; Rach, Randolph C. 3 2016 On continuous approximate solutions of nonlinear differential equations. Zbl 0633.34010 Rach, R. 2 1987 Evaluation of integrals by decomposition. Zbl 0648.65063 Adomian, G.; Rach, R. 2 1988 An application of the decomposition method to the matrix Riccati equation in a neutron transport process. Zbl 0673.34007 Adomian, G.; Pandolfi, M.; Rach, R. 2 1988 Purely nonlinear differential equations. Zbl 0698.34013 Adomian, G.; Rach, R. 2 1990 A coupled nonlinear system. Zbl 0616.65054 Adomian, G.; Rach, R. 2 1986 Simulation of large deflections of a flexible cantilever beam fabricated from functionally graded materials by the Adomian decomposition method. Zbl 1474.74002 Rach, Randolph; Duan, Jun-Sheng; Wazwaz, Abdul-Majid 2 2020 On the existence, uniqueness, and new analytic approximate solution of the modified error function in two-phase Stefan problems. Zbl 1472.35463 Bougoffa, Lazhar; Rach, Randolph C.; Mennouni, Abdelaziz 2 2021 Explicit solutions for differential equations. Zbl 0635.34003 Adomian, G.; Rach, R. 1 1987 On nonzero initial conditions in stochastic differential equations. Zbl 0552.60053 Adomian, G.; Rach, R. 1 1984 Exact and approximate analytic solutions of the nonlinear convective fin problem with temperature-dependent thermal conductivity. Zbl 1549.74020 Bougoffa, Lazhar; Mziou, Samy; Rach, Randolph C. 1 2017 Solving nonlocal boundary value problems for first- and second-order differential equations by the Adomian decomposition method. Zbl 1511.65075 Bougoffa, Lazhar; Rach, Randolph C. 1 2013 On approximate solution of a nonlinear differential equation. Zbl 0715.34021 Rach, R.; Baghdasarian, A. 1 1990 Simulation of the eigenvalue problem for tapered rotating beams by the modified decomposition method. Zbl 1541.74051 Duan, Jun-Sheng; Rach, Randolph; Wazwaz, Abdul-Majid 3 2022 On the existence, uniqueness, and new analytic approximate solution of the modified error function in two-phase Stefan problems. Zbl 1472.35463 Bougoffa, Lazhar; Rach, Randolph C.; Mennouni, Abdelaziz 2 2021 Simulation of large deflections of a flexible cantilever beam fabricated from functionally graded materials by the Adomian decomposition method. Zbl 1474.74002 Rach, Randolph; Duan, Jun-Sheng; Wazwaz, Abdul-Majid 2 2020 Evaluation of Gaussian integrals by Adomian decomposition. Zbl 1467.35097 Bougoffa, Lazhar; Rach, Randolph C. 1 2020 Higher order numeric solutions of the Lane-Emden-type equations derived from the multi-stage modified Adomian decomposition method. Zbl 1366.65069 Duan, Jun-Sheng; Rach, Randolph; Wazwaz, Abdul-Majid 10 2017 Exact and approximate analytic solutions of the nonlinear convective fin problem with temperature-dependent thermal conductivity. Zbl 1549.74020 Bougoffa, Lazhar; Mziou, Samy; Rach, Randolph C. 1 2017 On solutions of boundary value problem for fourth-order beam equations. Zbl 1488.34116 Bougoffa, Lazhar; Rach, Randolph; Wazwaz, Abdul-Majid 9 2016 Two reliable methods for solving the Volterra integral equation with a weakly singular kernel. Zbl 1416.65557 Wazwaz, Abdul-Majid; Rach, Randolph 7 2016 Variational iteration method for solving oxygen and carbon substrate concentrations in microbial floc particles. Zbl 1466.92118 Wazwaz, Abdul-Majid; Rach, Randolph; Duan, Jun-Sheng 6 2016 Exact and approximate analytic solutions of the Jeffery-Hamel flow problem by the Duan-Rach modified Adomian decomposition method. Zbl 1488.65180 Bougoffa, Lazhar; Mziou, Samy; Rach, Randolph C. 3 2016 Steady-state concentrations of carbon dioxide absorbed into phenyl glycidyl ether solutions by the Adomian decomposition method. Zbl 1323.34024 Duan, Jun-Sheng; Rach, Randolph; Wazwaz, Abdul-Majid 18 2015 Chaos control in the cerium-catalyzed Belousov-Zhabotinsky reaction using recurrence quantification analysis measures. Zbl 1352.93053 Fatoorehchi, Hooman; Zarghami, Reza; Abolghasemi, Hossein; Rach, Randolph 12 2015 On the Adomian decomposition method for solving the Stefan problem. Zbl 1356.80034 Bougoffa, Lazhar; Rach, Randolph; Wazwaz, Abdul-Majid; Duan, Jun-Sheng 8 2015 Solving new fourth-order Emden-Fowler-type equations by the Adomian decomposition method. Zbl 1549.34055 Wazwaz, Abdul-Majid; Rach, Randolph; Duan, Jun-Sheng 7 2015 Oxygen and carbon substrate concentrations in microbial floc particles by the Adomian decomposition method. Zbl 1468.92030 Duan, Jun-Sheng; Rach, Randolph; Wazwaz, Abdul-Majid 5 2015 Modeling the influence of the Casimir force on the pull-in instability of nanowire-fabricated nanotweezers. Zbl 1308.81158 Farrokhabadi, Amin; Mokhtari, Javad; Rach, Randolph; Abadyan, Mohamadreza 4 2015 The Volterra integral form of the Lane-Emden equation: new derivations and solution by the Adomian decomposition method. Zbl 1322.34022 Rach, Randolph; Wazwaz, Abdul-Majid; Duan, Jun-Sheng 4 2015 Solving coupled Lane-Emden boundary value problems in catalytic diffusion reactions by the Adomian decomposition method. Zbl 1311.92222 Rach, Randolph; Duan, Jun-Sheng; Wazwaz, Abdul-Majid 51 2014 A study on the systems of the Volterra integral forms of the Lane-Emden equations by the Adomian decomposition method. Zbl 1302.34024 Wazwaz, Abdul-Majid; Rach, Randolph; Duan, Jun-Sheng 23 2014 Solving the Lane-Emden-Fowler type equations of higher orders by the Adomian decomposition method. Zbl 1356.65214 Wazwaz, Abdul-Majid; Rach, Randolph; Bougoffa, Lazhar; Duan, Jun-Sheng 7 2014 A reliable analysis of oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics. Zbl 1330.92037 Rach, Randolph; Wazwaz, Abdul-Majid; Duan, Jun-Sheng 5 2014 An improved approximate analytic solution for Riccati equations over extended intervals. Zbl 1310.34022 Vahidi, A. R.; Didgar, M.; Rach, R. C. 3 2014 Adomian decomposition method for solving the Volterra integral form of the Lane-Emden equations with initial values and boundary conditions. Zbl 1282.65082 Wazwaz, Abdul-Majid; Rach, Randolph; Duan, Jun-Sheng 41 2013 A new modified Adomian decomposition method and its multistage form for solving nonlinear boundary value problems with Robin boundary conditions. Zbl 1426.65122 Duan, Jun-Sheng; Rach, Randolph; Wazwaz, Abdul-Majid; Chaolu, Temuer; Wang, Zhong 34 2013 The Adomian decomposition method with convergence acceleration techniques for nonlinear fractional differential equations. Zbl 1348.34010 Duan, Jun-Sheng; Chaolu, Temuer; Rach, Randolph; Lu, Lei 23 2013 Solving nonlocal initial-boundary value problems for linear and nonlinear parabolic and hyperbolic partial differential equations by the Adomian decomposition method. Zbl 1334.65177 Bougoffa, Lazhar; Rach, Randolph C. 12 2013 Solving Cauchy integral equations of the first kind by the Adomian decomposition method. Zbl 1416.65529 Bougoffa, Lazhar; Mennouni, Abdelaziz; Rach, Randolph C. 11 2013 A reliable modification of the Adomian decomposition method for higher-order nonlinear differential equations. Zbl 1511.65076 Rach, Randolph; Wazwaz, Abdul-Majid; Duan, Jun-Sheng 9 2013 On the effective region of convergence of the decomposition series solution. Zbl 1280.65083 Duan, Jun-Sheng; Rach, Randolph; Wang, Zhong 5 2013 A new modified Adomian decomposition method for higher-order nonlinear dynamical systems. Zbl 1356.65207 Duan, Jun-Sheng; Rach, Randolph; Wazwaz, Abdul-Majid 4 2013 Solving nonlocal initial-boundary value problems for the Lotka-von Foerster model. Zbl 1334.65178 Bougoffa, Lazhar; Rach, Randolph C.; Wazwaz, Abdul-Majid 4 2013 A convergence analysis of the Adomian decomposition method for an abstract Cauchy problem of a system of first-order nonlinear differential equations. Zbl 1321.65108 Bougoffa, Lazhar; Rach, Randolph C.; El-Manouni, Said 3 2013 Analytic approximation of the blow-up time for nonlinear differential equations by the ADM-Padé technique. Zbl 1283.34031 Duan, Jun-Sheng; Rach, Randolph; Lin, Shi-Ming 3 2013 Solving nonlocal boundary value problems for first- and second-order differential equations by the Adomian decomposition method. Zbl 1511.65075 Bougoffa, Lazhar; Rach, Randolph C. 1 2013 Solutions of the initial value problem for nonlinear fractional ordinary differential equations by the rach-Adomian-meyers modified decomposition method. Zbl 1245.65087 Duan, Jun-Sheng; Chaolu, Temuer; Rach, Randolph 19 2012 A bibliography of the theory and applications of the Adomian decomposition method, 1961–2011. Zbl 1511.65112 Rach, Randolph 19 2012 Advances in the Adomian decomposition method for solving two-point nonlinear boundary value problems with Neumann boundary conditions. Zbl 1247.65097 Aly, Emad H.; Ebaid, Abdelhalim; Rach, Randolph 9 2012 Higher-order numeric Wazwaz-El-Sayed modified Adomian decomposition algorithms. Zbl 1247.65109 Duan, Jun-Sheng; Rach, Randolph 6 2012 A convenient technique for solving integral equations of the first kind by the Adomian decomposition method. Zbl 1511.65145 Bougoffa, Lazhar; Al-Haqbani, Manal; Rach, Randolph C. 5 2012 A new modification of the Adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations. Zbl 1521.65071 Duan, Jun-Sheng; Rach, Randolph 59 2011 Comparison of the Adomian decomposition method and the variational iteration method for solving the Lane-Emden equations of the first and second kinds. Zbl 1511.65079 Wazwaz, Abdul-Majid; Rach, Randolph 25 2011 New higher-order numerical one-step methods based on the Adomian and the modified decomposition methods. Zbl 1478.65071 Duan, Jun-Sheng; Rach, Randolph 17 2011 Near-field and far-field approximations by the Adomian and asymptotic decomposition methods. Zbl 1209.65071 Rach, Randolph; Duan, Jun-Sheng 14 2011 A convenient technique for solving linear and nonlinear Abel integral equations by the Adomian decomposition method. Zbl 1252.65207 Bougoffa, Lazhar; Rach, Randolph C.; Mennouni, Abdelaziz 12 2011 An approximate method for solving a class of weakly-singular Volterra integro-differential equations. Zbl 1219.65159 Bougoffa, Lazhar; Rach, Randolph C.; Mennouni, Abdelaziz 10 2011 A new definition of the Adomian polynomials. Zbl 1176.33023 Rach, Randolph C. 60 2008 Numerical integration, analytic continuation, and decomposition. Zbl 0905.65079 Adomian, G.; Rach, R. C.; Meyers, R. E. 16 1997 Modified Adomian polynomials. Zbl 0874.65051 Adomian, G.; Rach, R. 40 1996 Modified decomposition solution of linear and nonlinear boundary-value problems. Zbl 0810.34015 Adomian, G.; Rach, R. 45 1994 Analytic solution of nonlinear boundary-value problems in serveral dimensions by decomposition. Zbl 0796.35017 Adomian, G.; Rach, R. 67 1993 A new algorithm for matching boundary conditions in decomposition solutions. Zbl 0780.65045 Adomian, G.; Rach, R. 16 1993 Solution of nonlinear partial differential equations in one, two, three, and four dimensions. Zbl 0834.65058 Adomian, G.; Rach, R. 5 1993 Noise terms in decomposition solution series. Zbl 0777.35018 Adomian, G.; Rach, R. 87 1992 A modified decomposition. Zbl 0756.35013 Rach, R.; Adomian, G.; Meyers, R. E. 36 1992 Generalization of Adomian polynomials to functions of several variables. Zbl 0765.34005 Adomian, G.; Rach, R. 21 1992 Nonlinear transformation of series. II. Zbl 0768.40001 Adomian, G.; Rach, R. 17 1992 Differential equations with singular coefficients. Zbl 0748.65066 Rach, R.; Baghdasarian, A.; Adomian, G. 12 1992 Modified decomposition solution of nonlinear partial differential equations. Zbl 0794.35023 Adomian, G.; Rach, R. 11 1992 A further consideration of partial solutions in the decomposition method. Zbl 0756.35012 Adomian, G.; Rach, R. 11 1992 Inhomogeneous nonlinear partial differential equations with variable coefficients. Zbl 0758.35023 Adomian, G.; Rach, R. 10 1992 Transformation of series. Zbl 0742.40004 Adomian, G.; Rach, R. 34 1991 An efficient methodology for the physical sciences. Zbl 0744.65039 Adomian, G.; Rach, R. C.; Meyers, R. E. 28 1991 Numerical algorithms and decomposition. Zbl 0728.65068 Adomian, G.; Rach, R.; Meyers, Ronald E. 13 1991 Solution of nonlinear ordinary and partial differential equations of physics. Zbl 0792.34006 Adomian, G.; Rach, R. 4 1991 Equality of partial solutions in the decomposition method for linear or nonlinear partial differential equations. Zbl 0702.35058 Adomian, G.; Rach, R. 54 1990 Multiple decompositions for computational convenience. Zbl 0707.34008 Rach, R.; Adomian, G. 7 1990 Purely nonlinear differential equations. Zbl 0698.34013 Adomian, G.; Rach, R. 2 1990 On approximate solution of a nonlinear differential equation. Zbl 0715.34021 Rach, R.; Baghdasarian, A. 1 1990 A new approach to boundary value equations and application to a generalization of Airy’s equation. Zbl 0678.65057 Adomian, G.; Elrod, M.; Rach, R. 13 1989 On the solution of partial differential equations with specified boundary conditions. Zbl 0678.65084 Adomian, G.; Rach, R.; Elrod, M. 12 1989 Smooth polynomial expansions of piecewise-differentiable functions. Zbl 0721.41043 Rach, R.; Adomian, G. 4 1989 Analytic parametrization and the decomposition method. Zbl 0754.60066 Adomian, G.; Rach, R. 3 1989 The decomposition method applied to stiff systems. Zbl 0645.65040 Adomian, G.; Rach, R.; Elrod, M. 5 1988 Evaluation of integrals by decomposition. Zbl 0648.65063 Adomian, G.; Rach, R. 2 1988 An application of the decomposition method to the matrix Riccati equation in a neutron transport process. Zbl 0673.34007 Adomian, G.; Pandolfi, M.; Rach, R. 2 1988 On the Adomian (decomposition) method and comparisons with Picard’s method. Zbl 0645.60067 Rach, R. 37 1987 On continuous approximate solutions of nonlinear differential equations. Zbl 0633.34010 Rach, R. 2 1987 Explicit solutions for differential equations. Zbl 0635.34003 Adomian, G.; Rach, R. 1 1987 On composite nonlinearities and the decomposition method. Zbl 0617.65046 Adomian, G.; Rach, R. 17 1986 The noisy convergence phenomena in decomposition method solutions. Zbl 0616.65084 Adomian, G.; Rach, R. 14 1986 Algebraic computation and the decomposition method. Zbl 0604.60064 Adomian, G.; Rach, R. 13 1986 On linear and nonlinear integro-differential equations. Zbl 0601.45009 Adomian, G.; Rach, R. 12 1986 Solving nonlinear differential equations with decimal power nonlinearities. Zbl 0591.60052 Adomian, G.; Rach, R. 7 1986 On the solution of nonlinear differential equations with convolution product nonlinearities. Zbl 0588.34004 Adomian, G.; Rach, R. 6 1986 A new computational approach for inversion of very large matrices. Zbl 0613.65023 Adomian, G.; Rach, R. 5 1986 A coupled nonlinear system. Zbl 0616.65054 Adomian, G.; Rach, R. 2 1986 On the solution of algebraic equations by the decomposition method. Zbl 0552.60060 Adomian, G.; Rach, R. 58 1985 Polynomial nonlinearities in differential equations. Zbl 0606.34009 Adomian, G.; Rach, R. 22 1985 On the solution of equations containing radicals by the decomposition method. Zbl 0579.60060 Adomian, G.; Rach, R.; Sarafyan, D. 11 1985 Coupled differential equations and coupled boundary conditions. Zbl 0579.60057 Adomian, G.; Rach, R. 9 1985 Application of the decomposition method to inversion of matrices. Zbl 0598.65011 Adomian, G.; Rach, R. 9 1985 Algebraic equations with exponential terms. Zbl 0579.60058 Adomian, G.; Rach, R. 7 1985 Nonlinear differential equations with negative power nonlinearities. Zbl 0579.60059 Adomian, G.; Rach, R. 7 1985 Nonlinear plasma response. Zbl 0575.60063 Adomian, G.; Rach, R. 3 1985 A convenient computational form for the Adomian polynomials. Zbl 0552.60061 Rach, Randolph 86 1984 On nonzero initial conditions in stochastic differential equations. Zbl 0552.60053 Adomian, G.; Rach, R. 1 1984 Inversion of nonlinear stochastic operators. Zbl 0504.60066 Adomian, G.; Rach, R. 159 1983 Nonlinear stochastic differential delay equations. Zbl 0504.60067 Adomian, G.; Rach, R. 106 1983 A nonlinear differential delay equation. Zbl 0504.60068 Adomian, G.; Rach, R. 10 1983 Coupled nonlinear stochastic differential equations. Zbl 0517.60064 Adomian, G.; Sibul, L. H.; Rach, R. 7 1983 ...and 1 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,153 Authors 88 Adomian, George 77 Rach, Randolph C. 47 Wazwaz, Abdul-Majid Abdul-Rahman 26 Duan, Junsheng 25 Singh, Randhir 24 Cherruault, Yves 15 Bougoffa, Lazhar 13 Lesnic, Daniel 12 Kumar, Jitendra 11 Abbasbandy, Saeid 10 Băleanu, Dumitru I. 10 Ramos, Juan I. 9 Ganji, Davood Domiri 8 Bellomo, Nicola 8 Fatoorehchi, Hooman 8 Inc, Mustafa 7 Abolghasemi, Hossein 7 Dehghan Takht Fooladi, Mehdi 7 Ebaid, Abdelhalim 7 El-Kalla, Ibrahim L. 7 Khuri, Suheil A. 7 Vellaisamy, Palaniappan 7 Verma, Amit Kumar 6 Abbaoui, Karim 6 Al-Hayani, Waleed 6 Babolian, Esmail 6 Biazar, Jafar 6 Kaya, Doǧan 6 Khan, Arshad 6 Kiliçman, Adem 6 Meyers, Ronald E. 6 Nelakanti, Gnaneshwar 6 Ramos, Higinio 6 Riganti, Riccardo 6 Sabir, Zulqurnain 5 Casasús, Luis 5 Chaolu, Temuer 5 Evans, David John 5 Gómez-Aguilar, José Francisco 5 Kataria, Kuldeep Kumar 5 Raja, Muhammad Asif Zahoor 5 Ziada, E. A. A. 4 Aghazadeh, Nasser 4 Bildik, Necdet 4 Bonzani, Ida 4 Bulut, Hasan 4 Cattani, Carlo 4 Chun, Changbum 4 El-Sayed, Salah M. 4 Gabet, Lionel 4 González-Gaxiola, Oswaldo 4 Heydari, Mohammad Mehdi 4 Islam, Saeed 4 Jafari, Hossein 4 Jang, Bongsoo 4 Kumar, Rajesh 4 Loghmani, Ghasem Barid 4 Luo, Xingguo 4 Mohammadi, Amir Hossein Mousavi 4 Monaco, Roberto 4 Motsa, Sandile Sydney 4 Noorani, Mohd Salmi Mohd 4 Ray, Sumita Saha 4 Rèpaci, Antonino 4 Sezer, Mehmet 4 Singh, Mehakpreet 4 Wang, Tongke 4 Yıldırım, Ahmet 3 Abassy, Tamer A. 3 Abdullah, Farah Aini 3 Barnwal, Amit K. 3 Ben Zitoun, Feyed 3 Bera, Rasajit K. 3 Cafagna, Donato 3 Cordero, Alicia 3 Dang, Chuangyin 3 Darvishi, Mohammad Taghi 3 Delkhosh, Mehdi 3 El-Sayed, Ahmed Mohamed Ahmed 3 Escobar-Jiménez, Ricardo Fabricio 3 García Guirao, Juan Luis 3 García-Olivares, Antonio 3 Gorguis, Alice 3 Grassi, Giuseppe 3 Hasan, Yahya Qaid 3 Hashim, Ishak 3 Huang, Lanlan 3 Hussain, Saddam 3 Jiao, Yongchang 3 Khalique, Chaudry Masood 3 Khanfer, Ammar 3 Khelifa, Salim 3 Kong, Lingju 3 Kurkcu, Omur Kivanc 3 Liao, Shijun 3 Lin, Guoxing 3 Liu, Yinping 3 Madera, Aleksandr Georgievich 3 Makarov, Volodymyr Leonidovych 3 Marczak, Rogério José ...and 1,053 more Authors all top 5 Cited in 185 Serials 133 Applied Mathematics and Computation 57 Journal of Mathematical Analysis and Applications 49 Computers & Mathematics with Applications 30 International Journal of Computer Mathematics 29 International Journal of Applied and Computational Mathematics 26 Journal of Computational and Applied Mathematics 25 Journal of Mathematical Chemistry 24 Applied Mathematics Letters 23 Kybernetes 23 Mathematical and Computer Modelling 22 Mathematical Problems in Engineering 22 Communications in Nonlinear Science and Numerical Simulation 21 Mathematical Methods in the Applied Sciences 20 Journal of Applied Mathematics and Computing 17 Chaos, Solitons and Fractals 17 Applied Mathematical Modelling 16 Abstract and Applied Analysis 15 Mathematics and Computers in Simulation 14 Computational and Applied Mathematics 10 Applied Numerical Mathematics 10 Journal of the Egyptian Mathematical Society 10 Advances in Difference Equations 7 Numerical Methods for Partial Differential Equations 7 Discrete Dynamics in Nature and Society 6 Journal of Applied Mathematics 6 Advances in Mathematical Physics 5 International Journal of Modern Physics B 5 Computer Methods in Applied Mechanics and Engineering 5 Acta Applicandae Mathematicae 5 Numerical Algorithms 5 International Journal of Computational Methods 5 Mathematical Sciences 5 AIMS Mathematics 4 Computer Physics Communications 4 Physics Letters. 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Physical Sciences 2 MATCH - Communications in Mathematical and in Computer Chemistry 2 International Journal of Wavelets, Multiresolution and Information Processing 2 The Australian Journal of Mathematical Analysis and Applications 2 Boundary Value Problems 2 Advances and Applications in Discrete Mathematics 2 Advances in Differential Equations and Control Processes 2 International Journal for Numerical Methods in Biomedical Engineering 2 S\(\vec{\text{e}}\)MA Journal 2 East Asian Journal on Applied Mathematics 2 Mathematics 2 Journal of Applied Mathematics, Statistics and Informatics 2 Journal of Function Spaces 2 Results in Applied Mathematics 1 Modern Physics Letters A 1 Modern Physics Letters B 1 Acta Mechanica 1 Discrete Applied Mathematics 1 International Journal of Control 1 International Journal of Heat and Mass Transfer 1 Journal of Computational Physics 1 Physics Reports 1 Reports on Mathematical Physics 1 Rocky Mountain Journal of Mathematics 1 Ukrainian Mathematical Journal 1 ZAMP. 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