An application for linear and nonlinear heat equations by Adomian’s decomposition method. (English) Zbl 1060.65653

Summary: The particular exact solutions of a linear heat equation, and a nonlinear heat equation that usually arises in mathematical biology are obtained in both \(x\) and \(t\) directions using Adomian’s decomposition method. In addition, numerical comparison of particular solutions in the decomposition method for linear and nonlinear problems indicates that there is a good agreement between the numerical solutions and particular exact solutions in terms of accuracy and efficiency.


65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35K57 Reaction-diffusion equations
35K05 Heat equation
92E20 Classical flows, reactions, etc. in chemistry
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