A numerical study of the Burgers’ and Fisher’s equations using barycentric interpolation method

Abstract

PurposeThe purpose of the method is to develop a numerical method for the solution of nonlinear partial differential equations.Design/methodology/approachA new numerical approach based on Barycentric Rational interpolation has been used to solve partial differential equations.FindingsA numerical technique based on barycentric rational interpolation has been developed to investigate numerical simulation of the Burgers’ and Fisher’s equations. Barycentric interpolation is basically a variant of well-known Lagrange polynomial interpolation which is very fast and stable. Using semi-discretization for unknown variable and its derivatives in spatial direction by barycentric rational interpolation, we get a system of ordinary differential equations. This system of ordinary differential equation’s has been solved by applying SSP-RK43 method. To check the efficiency of the method, computed numerical results have been compared with those obtained by existing methods. Barycentric method is able to capture solution behavior at small values of kinematic viscosity for Burgers’ equation.Originality/valueTo the best of the authors’ knowledge, the method is developed for the first time and validity is checked by stability and error analysis.