Numerical study of Fisher's equation by wavelet Galerkin method

Abstract

Fisher's equation, which describes the logistic growth–diffusion process and occurs in many biological and chemical processes, has been studied numerically by the wavelet Galerkin method. Wavelets are functions which can provide local finer details. The solution of Fisher's equation has a compact support property and therefore Daubechies' compactly supported wavelet basis has been used in this study. The results obtained by the present method are highly encouraging and can be computed for a large value of the linear growth rate.

Keywords:

• Fisher's equation
• Partial differential equation
• Compactly supported Daubechies wavelet
• Wavelet Galerkin method

Acknowledgements

The second author gratefully acknowledges the financial support provided by the Council of Scientific and Industrial Research, New Delhi (India).

The authors gratefully acknowledge the suggestions given by the referees to improve the quality of the paper.