Application of TAGE Iterative Methods for the Solution of Nonlinear Two Point Boundary Value Problems with Linear Mixed Boundary Conditions on a Non-Uniform Mesh

Abstract

We report the application of two parameter alternating group explicit (TAGE) iteration and Newton-TAGE iteration methods for the solution of nonlinear differential equation u″=F(x, u, u′) subject to linear mixed boundary conditions on a non-uniform mesh. In both cases, we use only three non-uniform grid points. The convergence theory for TAGE iteration method is analyzed. Numerical examples are considered to demonstrate computationally and the utility of TAGE iteration methods.

Keywords:

• Non-uniform mesh
• Linear mixed boundary conditions
• TAGE method
• Newton-TAGE method
• SOR method
• Burgers’ equation

Acknowledgments

This research was supported by The Council of Scientific and Industrial Research under research grant No. 09/045(0836)2009-EMR-I.