On the Hybrid of Fourier Transform and Adomian Decomposition Method for the Solution of Nonlinear Cauchy Problems of the Reaction-Diffusion Equation


Creative Commons License

NOURAZAR S., NAZARI-GOLSHAN A., Yildirim A. , NOURAZAR M.

ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, vol.67, pp.355-362, 2012 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 67
  • Publication Date: 2012
  • Doi Number: 10.5560/zna.2012-0025
  • Title of Journal : ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES
  • Page Numbers: pp.355-362
  • Keywords: Cauchy Reaction-Diffusion, Fourier Transformation, Adomian Decomposition Method, Non-Homogeneous Partial Differential Equation, VARIATIONAL ITERATION METHOD, FLOW

Abstract

The physical science importance of the Cauchy problem of the reaction-diffusion equation appears in the modelling of a wide variety of nonlinear systems in physics, chemistry, ecology, biology, and engineering. A hybrid of Fourier transform and Adomian decomposition method (FTADM) is developed for solving the nonlinear non-homogeneous partial differential equations of the Cauchy problem of reaction-diffusion. The results of the FTADM and the ADM are compared with the exact solution. The comparison reveals that for the same components of the recursive sequences, the errors associated with the FTADM are much lesser than those of the ADM. We show that as time increases the results of the FTADM approaches 1 with only six recursive terms. This is in agreement with the physical property of the density-dependent nonlinear diffusion of the Cauchy problem which is also in agreement with the exact solution.