A third-order-accurate variable-mesh TAGE iterative method for the numerical solution of two-point non-linear singular boundary value problems

Abstract

We propose a third-order-accurate variable-mesh two-parameter alternating group explicit (TAGE) iteration method for the numerical solution of the two-point singular boundary value problem

subject to boundary conditions u(0)=A, u(1)=B, where A and B are finite constants. We also discuss a Newton–TAGE iteration method for the third-order numerical solution of a two-point non-linear boundary value problem. The proposed method is applicable to singular and non-singular problems and is suitable for use on parallel computers. The convergence analysis is briefly discussed. Computational results are provided to illustrate the proposed TAGE iterative methods.

Keywords:

• Variable mesh
• Third-order method
• TAGE method
• Newton–TAGE method
• Singular equation
• Convection diffusion equation
• Burgers equation