Abstract
In this paper, we discuss about some basic things of boundary value problems. Secondly, we study boundary conditions involving derivatives and obtain finite difference approximations of partial derivatives of boundary value problems. The last section is devoted to determine an approximate solution for boundary value problems using Variational Iteration Method (VIM)and discuss the basic idea of He’s Variational Iteration Method and its applications.Keywords: Boundary value problem, Boundary conditions, Variational Iteration Method, He’s Variational Iteration Method, Finite difference method, Standard 5-point formula, Iteration method, Relaxation method and standard analytic method.
Highlights
Solutions of Boundary Value Problems can sufficiently closely be approximated by simple and efficient numerical methods
© CNCS, Mekelle University length L= 1, which is clamped at its left side x= 0, and resting on an elastic bearing at its right side x =1, and adding a load f along its length to cause deformations, Ma and Silva [2004] arrived at the following boundary value problem assuming an EI = 1: (1.3)
This study showed that the finite difference method for the solution of a two point boundary value problem consists in replacing the derivatives present in the differential equation and the boundary conditions with the help of finite difference approximations and solving the resulting linear system of equations by a standard method
Summary
Solutions of Boundary Value Problems can sufficiently closely be approximated by simple and efficient numerical methods. Among these numerical methods are finite difference method, standard 5-point formula, iteration method, relaxation method and standard analytic method. There exist several methods to solve second order boundary value problem One of these is the finite difference method, which is most popular. Deng and Levine (2000) studied about the role of critical exponents in blow-up theorems. Qi (1991) studied the asymptotics of blow-up solutions of a degenerate parabolic equations. Zhang (1997) achieved on blow-up of solutions for a class of nonlinear reaction diffusion equations Le Roux (2000) derived a numerical solution of nonlinear reaction diffusion processes. Levine (1990) identified the role of critical exponents in blow-up theorems. Mochizuki and Suzuki (1997) find a critical exponents and critical blow up for quasi-linear parabolic equations. Qi (1991) studied the asymptotics of blow-up solutions of a degenerate parabolic equations. Samarskii et al (1995) observed a blow-up in quasilinear parabolic equations. Sperp (1980) studied the maximum principles and their applications. Zhang (1997) achieved on blow-up of solutions for a class of nonlinear reaction diffusion equations
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