10.1186/2251-7456-7-12

Numerical solutions of nonlinear Fisher's reaction–diffusion equation with modified cubic B-spline collocation method

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  • Ramesh Chand Mittal1,
  • Rakesh Kumar Jain*1,
  1. Department of Mathematics, I. I. T. Roorkee, Roorkee, Uttarakhand, 247667, IN
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Published in Issue 2013-02-23

How to Cite

Mittal, R. C., & Jain, R. K. (2013). Numerical solutions of nonlinear Fisher’s reaction–diffusion equation with modified cubic B-spline collocation method. Mathematical Sciences, 7(1). https://doi.org/10.1186/2251-7456-7-12
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Abstract

Abstract In this paper, a numerical method is proposed to approximate the numeric solutions of nonlinear Fisher's reaction–diffusion equation with modified cubic B-spline collocation method. The method is based on collocation of modified cubic B-splines over finite elements, so we have continuity of the dependent variable and its first two derivatives throughout the solution range. We apply modified cubic B-splines for spatial variable and derivatives, which produce a system of first-order ordinary differential equations. We solve this system by using SSP-RK54 scheme. The proposed method needs less storage space that causes less accumulation of numerical errors. The numerical approximate solution to the nonlinear Fisher's reaction–diffusion equation has been computed without using any transformation and linearization process. Illustrative three test examples are included to establish the effectiveness and pertinence of the technique. Easy and economical implementation is the strength of this method.

Keywords

  • Nonlinear Fisher's reaction–diffusion equation,
  • Modified cubic B-spline basis functions,
  • SSP-RK54 scheme,
  • Thomas algorithm
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