ABSTRACT
Under appropriate assumptions, the transferral of genetic information is governed by a nonlinear reaction-diffusion equation, the generalized Fisher equation. This chapter deals with approximating this equation to a high degree of accuracy. The method of approach to the numerical solution of the generalized Fisher equation is comprised of a hybridization of Mehrstellenverfahren spatial discretization with Runge-Kutta time stepping. The chapter outlines the relevant biological, mathematical, and numerical models, and the efficacy of this approach is underscored by numerical examples from population genetics. It extends fourth-order accurate scheme to the generalized Fisher equation, thus accommodating arbitrary heterozygote fitness.
