An 0(h6) Finite Difference Analogue for the Numerical Solution of a Two Point Boundary Value Problem

1971 ◽  
Vol 8 (3) ◽  
pp. 335-343 ◽  
Author(s):  
RIAZ A. USMANI
Keyword(s):  
Finite Difference ◽  
Boundary Value Problem ◽  
Numerical Solution ◽  
Boundary Value ◽  
Point Boundary ◽  
Difference Analogue

scholarly journals Splitting least squares and collocation procedures for two-point boundary value problems

1985 ◽  
Vol 27 (2) ◽  
pp. 167-193
Author(s):  
John Locker ◽  
P. M. Prenter
Keyword(s):  
Linear System ◽  
Boundary Value Problem ◽  
Numerical Solution ◽  
Least Squares ◽  
Boundary Value ◽  
Linear Operators ◽  
Point Boundary ◽  
System Error ◽  
Densely Defined ◽  
Split System

AbstractLet L, T, S, and R be closed densely defined linear operators from a Hubert space X into X where L can be factored as L = TS + R. The equation Lu = f is equivalent to the linear system Tv + Ru = f and Su = v. If Lu = f is a two-point boundary value problem, numerical solution of the split system admits cruder approximations than the unsplit equations. This paper develops the theory of such splittings together with the theory of the Methods of Least Squares and of Collocation for the split system. Error estimates in both L2 and L∞ norms are obtained for both methods.

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

2017 ◽  
Vol 4 (1) ◽  
Author(s):  
Olufemi Bosede ◽  
Ashiribo Wusu ◽  
Moses Akanbi
Keyword(s):  
Mathematical Modeling ◽  
Differential Equation ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Finite Difference Methods ◽  
Stability And Convergence ◽  
Point Boundary ◽  
Difference Methods ◽  
The Stability

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.

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