Finite Difference Method for Approximate Solution of a Boundary Value Problem with Interior Singular Point

Abstract

This study is aimed at finding the approximate solutions of some boundary value problems with interior singular points. The considered problems differs from the standart boundary value problems in that they contains additional transmission conditions at the points of singularity. Naturally, such type of problems are much more complicate to solve than regular boundary value problems ones. Moreover, it is not clear how to apply the classical numerical methods to problems, involving not only boundary conditions at the end points of the considered interval, but also additional transmission conditions at some interior points. By modifying the Finite Diferrence Method we present a new numerical algoritm to find approximate solutions of the considered boundary value transmission problems. The obtained approximate solutions are compared with the exact solutions for some illustrative singular boundary value problems, involving additional transmission conditions. To justify the proposed modification some graphical illustrations of the approximate solutions are also presented.

Keywords

• Finite difference method
• boundary value problems
• transmission conditions
• interior singular point

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