Research Article Open Access

On the Closed Form Solutions of Linear and Nonlinear Cauchy Reaction-Diffusion Equations Using the Hybrid of Fourier Transform and Variational Iteration Method

S.S. Nourazar1, A. Nazari-Golshan2 and M. Nourazar3
  • 1 ,
  • 2 Amirkabir University of Technology, Iran
  • 3 Azad Islamic University, Iran
Physics International
Volume 2 No. 1, 2011, 8-20

DOI: https://doi.org/10.3844/pisp.2011.8.20

Submitted On: 25 June 2011 Published On: 26 October 2011

How to Cite: Nourazar, S., Nazari-Golshan, A. & Nourazar, M. (2011). On the Closed Form Solutions of Linear and Nonlinear Cauchy Reaction-Diffusion Equations Using the Hybrid of Fourier Transform and Variational Iteration Method. Physics International, 2(1), 8-20. https://doi.org/10.3844/pisp.2011.8.20

Abstract

Problem statement: In the present study, a hybrid of Fourier transform and Variational Iteration Method (FTVIM) is developed for solving the non-homogeneous linear and nonlinear partial differential equations of Cauchy reaction-diffusion problem. Approach: The closed form solutions obtained from the series solution of recursive sequences is valid for the entire range of problem domain. Results and Conclusion: Moreover, the very rapid convergence towards the exact solutions using the new method, FTVIM, indicates that the amount of computational work is much less than the computational work required for both the previous VIMs and the modified VIMs.

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Keywords

  • Cauchy reaction-diffusion
  • fourier transformation
  • variational iteration method
  • Non-homogeneous
  • partial differential equation
  • exact solutions
  • restricted variational