Experimentation with two-step Adomian decomposition method to solve evolution models

DOI10.1016/j.amc.2005.08.029zbMath1093.65100OpenAlexW2144731177MaRDI QIDQ2493722

Xing-Guo Luo, Bing-Quan Zhang, Qing-Biao Wu

Publication date: 16 June 2006

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2005.08.029

zbMATH Keywords

numerical examplesAdomian decomposition methodhyperbolic partial differential equationssingular initial value problemssystems of inhomogeneous differential and integral equations

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Other nonlinear integral equations (45G10) Nonlinear ordinary differential equations and systems (34A34) Second-order nonlinear hyperbolic equations (35L70) Numerical methods for initial value problems involving ordinary differential equations (65L05) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

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Computation of the general relativistic perihelion precession and of light deflection via the Laplace-Adomian decomposition method ⋮ An analytical solution of linear/nonlinear fractional-order partial differential equations and with new existence and uniqueness conditions ⋮ Symbolic computation of analytic approximate solutions for nonlinear differential equations with initial conditions ⋮ A Jacobi-Gauss collocation method for solving nonlinear Lane-Emden type equations ⋮ ADMP: a Maple package for symbolic computation and error estimating to singular two-point boundary value problems with initial conditions ⋮ Solution of the heat equation with variable properties by two-step Adomian decomposition method ⋮ An approximation algorithm for the solution of the nonlinear Lane-Emden type equations arising in astrophysics using Hermite functions collocation method ⋮ The restrictions and improvement of the Adomian decomposition method ⋮ Unnamed Item ⋮ Revisit on partial solutions in the Adomian decomposition method: solving heat and wave equations ⋮ Solution of Lane-Emden type equations using rational Bernoulli functions

Cites Work

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• New results for convergence of Adomian's method applied to integral equations
• Noise terms in decomposition solution series
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• A new computational method for Laplace transforms by decomposition method.
• The solution of two dimensional nonlinear differential equation by the Adomian decomposition method
• An approximation to the solution of hyperbolic equations by Adomian decomposition method and comparison with characteristics method
• Nonlinear stochastic differential delay equations
• A new method for solving singular initial value problems in the second-order ordinary differential equations
• Application of the Adomian decomposition method for two-dimensional parabolic equation subject to nonstandard boundary specifications
• An analytic study of Fisher's equation by using Adomian decomposition method
• A new algorithm for solving classical Blasius equation
• An application of the ADM to seven-order Sawada--Kotara equations
• A two-step Adomian decomposition method
• A review of the decomposition method and some recent results for nonlinear equations

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