Numerical solution of Fisher's equation using a moving mesh method
As it is well-known, \textit{R. A. Fisher} [The wave of advance of advantageous genes. Ann. Eugenics 7, 355 (1937)] introduced a nonlinear parabolic partial differential equation on an initial spating domain to model the simultaneous growth and spread of a dominant gene. In this paper, the two objectives are discussed. The first is to investigate the viability of moving mesh finite difference methods for the approximate solution of the challenging problem. The second objective is to make comparison between the moving mesh partial differential equation method proposed by \textit{W. Huang}, \textit{Y. Ren} and \textit{R. D. Russel} [SIAM J. Numer. Anal. 31, No. 3, 709-730 (1994; Zbl 0806.65092)] and the moving mesh differential-algebraic equation method proposed by \textit{L. S. Mulholland}, \textit{Y. Qiu} and \textit{D. M. Sloan} [J. Comput. Phys. 131, No. 2, 280-298 (1997; Zbl 0868.65057)].
simultaneous growth and spread of a dominant gene
scientific article; zbMATH DE number 1240706