Finite-difference methods for solution of nonlocal boundary value problems

Finite Difference Solution of Mixed Boundary-value Elastic Problems

A new numerical method of solution has been developed for the analysis of deformation and stresses in elastic bodies subjected to mixed boundary-conditions. The program is capable of dealing with both regular and irregular shapes of boundaries appropriately. An ideal mathematical model, based on the displacement potential function, has been used in the finite difference solution. The present pa...

Nonlocal Boundary Value Problems

The theory of the nonlocal linear boundary value problems is still on the level of examples. Any attempt to encompass them by a unified scheme sticks upon the lack of general methods. Here we are to outline an algebraic approach to linear nonlocal boundary value problems. It is based on the notion of convolution of linear operator and on operational calculus on it. Our operators are right inver...

Numerical Solution for Boundary Value Problem Using Finite Difference Method

In this paper, Numerical Methods for solving ordinary differential equations, beginning with basic techniques of finite difference methods for linear boundary value problem is investigated. Numerical solution is found for the boundary value problem using finite difference method and the results are compared with analytical solution. MATLAB coding is developed for the finite difference method. T...

Nonlocal Elliptic Boundary Value Problems

On the convergence of finite difference methods for weakly regular singular boundary value problems

The second order finite difference methods M1 based on a non-uniform mesh and M2 based on an uniform mesh developed by Chawla andKatti [Finite differencemethods and their convergence for a class of singular two point boundary value problems, Numer. Math. 39 (1982) 341–350] for weakly regular singular boundary value problems (p(x)y′)′ = f (x, y), 0<x 1, with p(x)= xb0 , 0 b0< 1, and boundary con...