Title: Spline method for solving generalised Fisher-Kolomogrov-Petrovskii-Piskunov equation

Authors: Kai Qu; Zhilei Zhao; Bo Jiang

Addresses: Department of Mathematics, Dalian Maritime University, Dalian 116026, China ' Navigation College, Dalian Maritime University, Dalian 116026, China ' Information Science and Technology College, Dalian Maritime University, Dalian 116026, China

Abstract: A numerical method (the finite element method using bivariate spline for generalised FKPP equation, FBG method for short), using bivariate splines, is presented for the numerical solution of a generalised Fisher-Kolomogrov-Petrovskii-Piskunov (FKPP) equation. In this paper, we constructed the bivariate spline proper subspace of S^2,3₄(Δ ⁽²⁾_mn), which satisfies homogeneous boundary conditions on type-2 triangulations. Also, we use S^2,3₄(Δ ⁽²⁾_mn) to interpolate the boundary conditions. An example is solved to assess the accuracy of the method. The numerical solutions obtained indicate that FBG method is reliable and yields results compatible with the exact solutions and consistent with other existing numerical methods.

Keywords: Fisher-Kolomogrov-Petrovskii-Piskunov equation; bivariate splines; integro-differential equation; finite element method; FEM; computer applications.

DOI: 10.1504/IJCAT.2014.066741

International Journal of Computer Applications in Technology, 2014 Vol.50 No.3/4, pp.276 - 280

Published online: 07 Feb 2015 *

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