Numerical Solution of One Boundary Value Problem Using Finite Difference Method

Authors : Oktay MUKHTAROV, Semih ÇAVUŞOĞLU, Hayati OLĞAR

Pages : 85-89

View : 45 | Download : 9

Publication Date : 2019-12-30

Article Type : Conference Paper

Abstract :Many problem of physics and engineering are modelled by boundary  value problems for ordinary or partial differential equations.  Usually, it is impossible to find the exact solution of the boundary  value problems, so we have to apply various numerical methods. There  are different numerical methods insert ignore into journalissuearticles values(for example, the Explicit Euler  method, the Runge-Kutta method, the Improved Euler method, Finite  difference method and finite element method); for determining the  approximate solutions of initial and boundary-value problems. One of  them is the finite difference method, which is the simplest scheme.  This method can be applied to higher of ordinary differential  equations, provided it is possible to write an explicit expression  for the highest order derivative and the system has a complete set  of initial conditions. In this study, we are interested in the  finite difference method for new type boundary value problems. We  describe the numerical solutions of some two-point boundary value  problems by using finite difference method. This method are based  upon the approximations that allow to replace the differential  equations by algebraic system of equations and the unknowns  solutions are related to grid points. In this article, we have  presented a finite difference method for solving second order  boundary value problems for ordinary differential equations with an  internal singularity. This method tested on several model problems  for the numerical solution.
Keywords : Finite difference method, boundary value problems, transmission conditions

ORIGINAL ARTICLE URL