scholarly journals Five-diagonal finite difference methods based on mixed-type interpolation for a certain fourth-order two-point boundary-value problem

1992 ◽  
Vol 24 (10) ◽  
pp. 55-76 ◽  
Author(s):  
M. Van Daele ◽  
G.Vanden Berghe ◽  
H. De Meyer
Keyword(s):  
Finite Difference ◽  
Boundary Value Problem ◽  
Fourth Order ◽  
Mixed Type ◽  
Boundary Value ◽  
Finite Difference Methods ◽  
Point Boundary ◽  
Type Interpolation ◽  
Difference 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.

scholarly journals Two new finite difference methods for computing eigenvalues of a fourth order linear boundary value problem

1987 ◽  
Vol 10 (3) ◽  
pp. 525-529 ◽  
Author(s):  
Riaz A. Usmani ◽  
Manabu Sakai
Keyword(s):  
Finite Difference ◽  
Boundary Value Problem ◽  
Fourth Order ◽  
Eigenvalue Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Finite Difference Methods ◽  
Practical Usefulness ◽  
Difference Methods ◽  
Linear Boundary Value Problem

This paper describes some new finite difference methods of order2and4for computing eigenvalues of a two-point boundary value problem associated with a fourth order differential equation of the form(py″)′​′+(q−λr)y=0. Numerical results for two typical eigenvalue problems are tabulated to demonstrate practical usefulness of our methods.

scholarly journals Finite difference methods for computing eigenvalues of fourth order boundary value problems

1986 ◽  
Vol 9 (1) ◽  
pp. 137-143 ◽  
Author(s):  
Riaz A. Usmani
Keyword(s):  
Differential Equation ◽  
Finite Difference ◽  
Fourth Order ◽  
Boundary Value ◽  
Finite Difference Methods ◽  
Order Linear Differential Equation ◽  
Point Boundary ◽  
Practical Usefulness ◽  
Difference Methods ◽  
Linear Differential

This brief report describes some new finite difference methods of order2and4for computing eigenvalues of a two point boundary value problem associated with a fourth order linear differential equationy(4)+(p(x)−λq(x))y=0. These methods are derived from the formulah4y1(4)=(δ4−16δ6+7240δ8−…)yi.Numerical results are included to demonstrate practical usefulness of our methods.

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