Symbolic computation of analytic approximate solutions for nonlinear differential equations with initial conditions

DOI10.1016/j.cpc.2011.08.001zbMath1263.65070OpenAlexW2071300255MaRDI QIDQ1947071

Yezhi Lin, Yin-Ping Liu, Zhi-Bin Li

Publication date: 12 April 2013

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cpc.2011.08.001

zbMATH Keywords

numerical examplesinitial value problemAdomian decomposition methodnonlinear integral equationBrusselator modelAdomian polynomialsanalytic approximate solutiontwo-step Adomian decomposition method

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Numerical methods for integral equations (65R20) Other nonlinear integral equations (45G10) Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99)

Related Items

A segmented and weighted Adomian decomposition algorithm for boundary value problem of nonlinear groundwater equation, \((n + 1)\)-dimensional reduced differential transform method for solving partial differential equations, Modified decomposition method with new inverse differential operators for solving singular nonlinear IVPs in first- and second-order PDEs arising in fluid mechanics

Uses Software

• Maple
• NAPA_

Cites Work

• On the variational iteration method
• A modified Adomian method for system of nonlinear differential equations
• Solution of the heat equation with variable properties by two-step Adomian decomposition method
• The solution of multipoint boundary value problems by the optimal homotopy asymptotic method
• A reliable modification of Adomian decomposition method
• Solving frontier problems of physics: the decomposition method
• Exact solutions for heat-like and wave-like equations with variable coefficients.
• The decomposition method applied to systems of partial differential equations and to the reaction-diffusion Brusselator model
• Construction of solitary wave solutions and rational solutions for the KdV equation by Adomian decomposition method
• New method for calculating Adomian polynomials
• The diffusion-Brusselator equation
• Application of Padé approximants to the study of plane jets
• Homotopy perturbation technique
• Solution of different type of the partial differential equation by differential transform method and Adomian's decomposition method
• Experimentation with two-step Adomian decomposition method to solve evolution models
• The decomposition method for stiff systems of ordinary differential equations
• A two-step Adomian decomposition method
• A new definition of the Adomian polynomials
• Beyond Perturbation