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Author ID: rach.randolph-c Recent zbMATH articles by "Rach, Randolph C."
Published as: Rach, R.; Rach, Randolph; Rach, Randolph C.; Rach, R. C.
Documents Indexed: 113 Publications since 1983
Co-Authors: 32 Co-Authors with 105 Joint Publications
511 Co-Co-Authors

Publications by Year

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 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
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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. A
4 International Journal of Mathematics and Mathematical Sciences
4 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
4 Soft Computing
4 Journal of Nonlinear Mathematical Physics
4 Mathematical Modelling and Analysis
4 International Journal of Biomathematics
4 International Journal of Differential Equations
3 Indian Journal of Pure & Applied Mathematics
3 Journal of the Franklin Institute
3 Stochastic Analysis and Applications
3 Computers and Mathematics with Applications. Part A
3 Journal of Mathematical Sciences (New York)
3 International Journal of Numerical Methods for Heat & Fluid Flow
3 Nonlinear Dynamics
3 Fractional Calculus & Applied Analysis
3 The ANZIAM Journal
3 Applications and Applied Mathematics
3 International Journal for Computational Methods in Engineering Science and Mechanics
3 Afrika Matematika
3 Journal of Applied Analysis and Computation
3 International Journal of Advances in Applied Mathematics and Mechanics
2 Computers and Fluids
2 International Journal of Engineering Science
2 International Journal of Mathematical Education in Science and Technology
2 Physica A
2 Statistics & Probability Letters
2 Physica D
2 Engineering Analysis with Boundary Elements
2 Chaos
2 European Journal of Mechanics. A. Solids
2 Russian Physics Journal
2 Nonlinear Functional Analysis and Applications
2 Computational Methods in Applied Mathematics
2 Proceedings of the National Academy of Sciences, India. Section A. 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. Zeitschrift für angewandte Mathematik und Physik
1 BIT
1 Calcolo
1 Demonstratio Mathematica
1 Gaṇita
1 Journal of Approximation Theory
1 Meccanica
...and 85 more Serials
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Cited in 43 Fields

549 Numerical analysis (65-XX)
307 Ordinary differential equations (34-XX)
267 Partial differential equations (35-XX)
94 Integral equations (45-XX)
57 Probability theory and stochastic processes (60-XX)
53 Fluid mechanics (76-XX)
53 Biology and other natural sciences (92-XX)
44 Real functions (26-XX)
39 Mechanics of deformable solids (74-XX)
29 Classical thermodynamics, heat transfer (80-XX)
24 Systems theory; control (93-XX)
20 Special functions (33-XX)
20 Approximations and expansions (41-XX)
20 Operator theory (47-XX)
19 Dynamical systems and ergodic theory (37-XX)
15 Integral transforms, operational calculus (44-XX)
14 Statistical mechanics, structure of matter (82-XX)
12 Computer science (68-XX)
9 Calculus of variations and optimal control; optimization (49-XX)
9 Quantum theory (81-XX)
8 Mechanics of particles and systems (70-XX)
8 Information and communication theory, circuits (94-XX)
6 Linear and multilinear algebra; matrix theory (15-XX)
6 Difference and functional equations (39-XX)
6 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
5 Optics, electromagnetic theory (78-XX)
5 Astronomy and astrophysics (85-XX)
5 Operations research, mathematical programming (90-XX)
4 Combinatorics (05-XX)
4 Sequences, series, summability (40-XX)
3 Functions of a complex variable (30-XX)
3 Harmonic analysis on Euclidean spaces (42-XX)
2 Number theory (11-XX)
2 Several complex variables and analytic spaces (32-XX)
2 Functional analysis (46-XX)
2 Relativity and gravitational theory (83-XX)
2 Geophysics (86-XX)
1 General and overarching topics; collections (00-XX)
1 Field theory and polynomials (12-XX)
1 Measure and integration (28-XX)
1 Algebraic topology (55-XX)
1 Statistics (62-XX)
1 Mathematics education (97-XX)

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