Abstract
The solutions of nonlinear heat equation with temperature dependent diffusivity are investigated using the modified Adomian decomposition method. Analysis of the method and examples are given to show that the Adomian series solution gives an excellent approximation to the exact solution. This accuracy can be increased by increasing the number of terms in the series expansion. The Adomian solutions are presented in some situations of interest.
Highlights
In the classical model of the heat equation, the thermal diffusivity and thermal conductivity of the medium are assumed to be constant
In this paper we investigate the nonlinear heat equation
The desired series solution by Adomian decomposition method is given by cf. 2–6 for details
Summary
In the classical model of the heat equation, the thermal diffusivity and thermal conductivity of the medium are assumed to be constant. In some media such as gases, these parameters are proportional to the temperature of the medium giving rise to a nonlinear heat equation of the following form 1 : C x. 1.3 with f u um, using the Adomian decomposition method This method was presented by Adomian to solve algebraic, differential, integrodifferential equations and stochastic problems 2–5. We will use the modified Adomian algorithm given by Wazwaz 10 to find the Adomian solutions to our models of nonlinear heat equation with temperature dependent diffusivity
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