Solution of linear and nonlinear heat equations by differential transform method. (English) Zbl 1229.65185

Summary: The differential transform method is one of the approximate methods which can be easily applied to many linear and nonlinear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. In this paper, we present the definition and operation of the two-dimensional differential transform and investigate the particular exact solutions of linear and nonlinear heat equations that usually arise in mathematical biology by two-dimensional differential transform method. The results of the present method are compared very well with those obtained by decomposition method.


65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
35K57 Reaction-diffusion equations