A Modified Laguerre Matrix Approach for Burgers–Fisher Type Nonlinear Equations

Abstract

Burgers–Fisher type nonlinear equations occur in many fields of science which describe a combination of reaction, convection and diffusion mechanisms with related to Burgers, Fisher and the generalized Burgers–Fisher equation also the Burgers–Fisher equation basically. In this study, we deal with a numerical technique which is called as a modified Laguerre matrix-collocation method in order to solve the Burgers–Fisher type nonlinear equations with initial and boundary conditions. Firstly, using this approach, we reduce the solution of nonlinear equation to the matrix form, which is the system of nonlinear algebraic equations with the unknown Laguerre coefficients. So that, the numerical solution of the problem is obtained by using the truncated Laguerre series. Furthermore, we provide a better approximation based on the error analysis. Illustrative examples are obtained in order to show the applicability and efficiency of the technique. Finally, we discuss the results shown by tables and figures.