An Efficient Wavelet-Based Approximation Method to Gene Propagation Model Arising in Population Biology

An Efficient Wavelet-Based Approximation Method to Gene Propagation Model Arising in Population... In this paper, we have applied an efficient wavelet-based approximation method for solving the Fisher’s type and the fractional Fisher’s type equations arising in biological sciences. To the best of our knowledge, until now there is no rigorous wavelet solution has been addressed for the Fisher’s and fractional Fisher’s equations. The highest derivative in the differential equation is expanded into Legendre series; this approximation is integrated while the boundary conditions are applied using integration constants. With the help of Legendre wavelets operational matrices, the Fisher’s equation and the fractional Fisher’s equation are converted into a system of algebraic equations. Block-pulse functions are used to investigate the Legendre wavelets coefficient vectors of nonlinear terms. The convergence of the proposed methods is proved. Finally, we have given some numerical examples to demonstrate the validity and applicability of the method. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Journal of Membrane Biology Springer Journals

An Efficient Wavelet-Based Approximation Method to Gene Propagation Model Arising in Population Biology

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Publisher
Springer US
Copyright
Copyright © 2014 by Springer Science+Business Media New York
Subject
Life Sciences; Biochemistry, general; Human Physiology
ISSN
0022-2631
eISSN
1432-1424
D.O.I.
10.1007/s00232-014-9672-x
Publisher site
See Article on Publisher Site

Abstract

In this paper, we have applied an efficient wavelet-based approximation method for solving the Fisher’s type and the fractional Fisher’s type equations arising in biological sciences. To the best of our knowledge, until now there is no rigorous wavelet solution has been addressed for the Fisher’s and fractional Fisher’s equations. The highest derivative in the differential equation is expanded into Legendre series; this approximation is integrated while the boundary conditions are applied using integration constants. With the help of Legendre wavelets operational matrices, the Fisher’s equation and the fractional Fisher’s equation are converted into a system of algebraic equations. Block-pulse functions are used to investigate the Legendre wavelets coefficient vectors of nonlinear terms. The convergence of the proposed methods is proved. Finally, we have given some numerical examples to demonstrate the validity and applicability of the method.

Journal

The Journal of Membrane BiologySpringer Journals

Published: Jun 8, 2014

References

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