Approximate Solutions of Fisher's Type Equations with Variable Coefficients

Abstract

The spectral collocation approximations based on Legendre polynomials are used to compute the numerical solution of timedependent Fisher's type problems. The spatial derivatives are collocated at a Legendre-Gauss-Lobatto interpolation nodes. The proposed method has the advantage of reducing the problem to a system of ordinary differential equations in time. The four-stage A-stable implicit Runge-Kutta scheme is applied to solve the resulted system of first order in time. Numerical results show that the Legendre-Gauss-Lobatto collocation method is of high accuracy and is efficient for solving the Fisher's type equations. Also the results demonstrate that the proposed method is powerful algorithm for solving the nonlinear partial differential equations.

Numerical Solution of Fisher’s Equation Using Finite Difference

“…Spectral methods (see, for instance, [7,8,9,10,11]) are powerful techniques that we use to numerically solve linear and nonlinear partial differential equations either in their strong or weak forms. Legendre Spectral Collocation Method is used to solve the Fisher's equation, see [12]. In [13], the author solve the Fisher's equation using PetrovGalerkin finite element method.…”