TY  - JOUR
T1  - Numerical Solution of One Boundary Value Problem Using Finite Difference Method
AU  - Çavuşoğlu, Semih
AU  - Mukhtarov, Oktay
AU  - Olğar, Hayati
PY  - 2019
DA  - December
JF  - Turkish Journal of Mathematics and Computer Science
JO  - TJMCS
PB  - Matematikçiler Derneği
WT  - DergiPark
SN  - 2148-1830
SP  - 85
EP  - 89
VL  - 11
LA  - en
AB  - Many problem of physics and engineering are modelled by boundaryvalue problems for ordinary or partial differential equations.Usually, it is impossible to find the exact solution of the boundaryvalue problems, so we have to apply various numerical methods. Thereare different numerical methods (for example, the Explicit Eulermethod, the Runge-Kutta method, the Improved Euler method, Finitedifference method and finite element method) for determining theapproximate solutions of initial and boundary-value problems. One ofthem is the finite difference method, which is the simplest scheme.This method can be applied to higher of ordinary differentialequations, provided it is possible to write an explicit expressionfor the highest order derivative and the system has a complete setof initial conditions. In this study, we are interested in thefinite difference method for new type boundary value problems. Wedescribe the numerical solutions of some two-point boundary valueproblems by using finite difference method. This method are basedupon the approximations that allow to replace the differentialequations by algebraic system of equations and the unknownssolutions are related to grid points. In this article, we havepresented a finite difference method for solving second orderboundary value problems for ordinary differential equations with aninternal singularity. This method tested on several model problemsfor the numerical solution.
KW  - Finite difference method
KW  - boundary value problems
KW  - transmission conditions
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UR  - https://dergipark.org.tr/en/pub/tjmcs/issue//613118
L1  - https://dergipark.org.tr/en/download/article-file/913503
ER  -