Volume 4, Issue 1

Stability and Convergence of Two-Step Obrechkoff Scheme For Second-Order Two-Point Boundary Value Problem

Olufemi Bosede1, Ashiribo Wusu2, and Moses Akanbi3
1Department Of Mathematics, Lagos State University, Ojo, Lagos State, Nigeria, Nigeria, 2Department Of Mathematics, Lagos State Univesity, Nigeria, and 3Department Of Mathematics, Lagos State Univesity, Nigeria
DOI:10.36108/jrrslasu/7102/40(0111)

Abstract


Mathematical modeling of scientific and engineering processes often yield Boundary Value Problems (BVPs). One of the broad categories of numerical methods for solving BVPs is the finite difference methods, in which the differential equation is replaced by a set of difference equations which are solved by direct or iterative methods. In this paper, we use some properties of matrices to analyze the stability and convergence of the prominent finite difference methods - two-step Obrechkoff method - for solving the boundary value problem $u^{\prime \prime} = f(t,u)$, $a < x < b$, $u(a) = \eta_1$, $u(b) = \eta_2$. Conditions for the stability and convergence of the two-step Obrechkoff method method were established.


Keywords: Convergence, Stability, Boundary Value Problem, Obrechkoff, and Finite Difference Scheme

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