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Comparison of TAGE and SOR Methods for Variable Mesh Arithmetic Average Discretization for Non-linear Two Point Boundary Value Problems with Mixed Boundary Conditions

R.K. Mohanty

Abstract



We discuss the comparison of two parameter alternating group explicit (TAGE) and successive over relaxation (SOR) iteration methods for an efficient third order variable mesh arithmetic average discretization for two point boundary value problems with mixed boundary conditions. We also discuss the application of Newton-TAGE algorithm for the non-linear system whose Jacobian is tri-diagonal. In all cases, we use only three grid points on a non-uniform mesh. The error analysis of the TAGE method is briefly discussed. The proposed TAGE and Newton-TAGE iteration methods are explicit in nature and coupled compactly, hence they are suitable for use on parallel computers. The effect of the proposed algorithms on non-uniform mesh is demonstrated by solving two test problems.

Keywords


Arithmetic average discretization, Variable mesh, TAGE and Newton-TAGE methods SOR method, Burgers’ equation, RMS errors.

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