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.

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 The Mathematical Modeling of Metals Mass Transfer in Three Layer Peat Blocks

2015 ◽  
Vol 1 ◽  
pp. 87
Author(s):  
Ērika Teirumnieka ◽  
Ilmārs Kangro ◽  
Edmunds Teirumnieks ◽  
Harijs Kalis
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Mass Transfer ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Mathematical Models ◽  
Boundary Value ◽  
Finite Difference Methods ◽  
Difference Methods ◽  
The Mathematical Model

The mathematical model for calculation of concentration of metals for 3 layers peat blocks is developed due to solving the 3-D boundary-value problem in multilayered domain-averaging and finite difference methods are considered. As an example, mathematical models for calculation of Fe and Ca concentrations have been analyzed.

Numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument

2017 ◽  
Vol 23 (2) ◽  
Author(s):  
Muhad H. Abregov ◽  
Vladimir Z. Kanchukoev ◽  
Maryana A. Shardanova
Keyword(s):  
Differential Equation ◽  
Numerical Methods ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Second Order ◽  
Deviating Argument ◽  
Second Order Differential Equation

AbstractThis work is devoted to the numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument in minor terms. The sufficient conditions of the one-valued solvability are established, and the a priori estimate of the solution is obtained. For the numerical solution, the problem studied is reduced to the equivalent boundary value problem for an ordinary linear differential equation of fourth order, for which the finite-difference scheme of second-order approximation was built. The convergence of this scheme to the exact solution is shown under certain conditions of the solvability of the initial problem. To solve the finite-difference problem, the method of five-point marching of schemes is used.

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