A new algorithm for the decomposition solution of nonlinear differential equations

DOI10.1016/j.camwa.2006.12.027zbMath1126.65059OpenAlexW1970535124MaRDI QIDQ2460602

I. L. El-Kalla, Ahmed Elsaid, S. H. Behiry, Hany Hashish

Publication date: 12 November 2007

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2006.12.027

zbMATH Keywords

nonlinear differential equationsBurgers equationKlein-Gordon equationAdomian decomposition methodsine-Gordon equationVan der Pol equationAdomian polynomials

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Nonlinear ordinary differential equations and systems (34A34) 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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Cites Work

• Convergence of Adomian's method
• A review of the decomposition method in applied mathematics
• Solving frontier problems of physics: the decomposition method
• A numerical solution of the sine-Gordon equation using the modified decomposition method
• An alternate algorithm for computing Adomian polynomials in special cases
• New method for calculating Adomian polynomials
• On the numerical solution of the system of two-dimensional Burgers' equations by the decomposition method
• Homotopy perturbation method for quadratic Riccati differential equation and comparison with Adomian's decomposition method
• A reliable symbolic implementation of algorithm for calculating Adomian polynomials
• Adomian method for solving some coupled systems of two equations
• A new algorithm for calculating Adomian polynomials
• Convergence of Adomian’s method applied to integral equations
• New numerical study of Adomian method applied to a diffusion model
• The modified decomposition method for analytic treatment of non-linear integral equations and systems of non-linear integral equations

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