Keywords : convergence analysis


Convergence Analysis of The Finite Difference Solution for Two Dimensions Coupled-Benjamin-Bona-Mahony System

Ekhlass S. Al-Rawi; Muhannad Shallal

AL-Rafidain Journal of Computer Sciences and Mathematics, 2013, Volume 10, Issue 2, Pages 129-141
DOI: 10.33899/csmj.2013.163480

This paper is devoted to drive the matrix algebraic equation for the two-dimensional nonlinear coupled-BBM system which is obtained from using the implicit finite difference method. The convergence analysis of the solution is proved.Numerical experiment is presented with initial conditions describing the generation and evolution.
 
 

Convergence Analysis of the Finite Difference Solution for the Nonlinear Klein-Gordon Equation

Ekhlass S. Al-Rawi

AL-Rafidain Journal of Computer Sciences and Mathematics, 2008, Volume 5, Issue 1, Pages 101-113
DOI: 10.33899/csmj.2008.163952

This paper is devoted to drive the matrix algebraic equation for the one-dimensional nonlinear Klein-Gordon equation which is obtained from using the implicit finite difference method. The convergence analysis of the solution is discussed. Numerical computations are conducted and the solutions are stable and convergent when the sine function is used as an initial condition.