AN SOR METHOD UTILIZING REDLICH-KISTER FINITE DIFFERENCE FOR TWO POINT BOUNDARY VALUE PROBLEMS
Keywords:
Boundary problem, Redlich-kister finite difference, SOR iteration, Two point boundary value problemsAbstract
This study presents a numerical method using a second-order Redlich-Kister Finite Difference (RKFD) discretization scheme to approximate the two-point boundary value problems (TPBVPs). The approach creates a linear system for the given problem by using the first two derivatives to create the RKFD approximation equation. Two iterative approaches are used to solve the linear system: Gauss-Seidel (GS) and Successive Over Relaxation (SOR). Two model examples that assess each approach according to its number of iterations, execution time, and maximum norm over five different mesh sizes indicate the effectiveness of these proposed iterative methods. The results show that the SOR method outperforms the GS methods in providing an extremely accurate approximation of the known exact solution.References
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