A Numerical Algorithm for the Computational Study of the Semi-Linear Parabolic Partial Differential Equations

Abstract

We investigate solutions of the two-dimensional semi-linear parabolic equations by a numerical method that employs cubic B- spline functions. Such type of equations arise in chemical reaction theory, mathematical biology, population dynamics, material science, and many other areas of science and engineering. The spirit of the method lies in the evaluation of first and second-order weighting coefficients by differential quadrature approximations. The two-dimensional equation has been discretized by the cubic B-spline differential quadrature method to obtain a system of ordinary differential equations(ODEs). A highly stability-preserving SSPRK-43 method has been applied to solve the system of ODEs. This method uses less storage which reduces the accumulation of numerical errors. Solutions computed by implementing the modified differential quadrature method have been presented graphically and in tabular form.