Coupled Reduced Alternating Group Explicit Algorithm for Third Order Cubic Spline Method on a Non-uniform Mesh for Nonlinear Singular Two Point Boundary Value Problems

Abstract

In this paper, we discuss the two parameter coupled reduced alternating group explicit (CRAGE) and Newton-CRAGE iteration methods to obtain the solution of viscous Burgers’ equation using a third order cubic spline numerical method, on non-uniform mesh. The proposed iterative methods are applicable to both singular and non-singular problems. The convergence of the CRAGE iteration method is discussed in detail. We have compared the results of proposed CRAGE iteration method with the results of corresponding two parameter alternating group explicit iterative method to demonstrate computationally the efficiency of the proposed method.