Modified Finite Difference Method for Solution of Two-interval Boundary Value Problems with Transition Conditions

Abstract

In this study, we have proposed a new modification of classical Finite Difference Method (FDM) for the solution of boundary value problems which are defined on two disjoint intervals and involved additional transition conditions at an common end of these intervals. The proposed modification of FDM differs from the classical FDM in calculating the iterative terms of numerical solutions. To illustrate the efficiency and reliability of the proposed modification of FDM some examples are solved. The obtained results are compared with those obtained by the standart FDM and by the analytical method. Corresponding graphical illustration are also presented.

A new finite difference algorithm for boundary value problems involving transmission conditions

“…Based on FDM, we have developed a new technique for solving two-interval boundary value problems (BVP), that included additional transmission conditions across the common endpoint of these intervals. We note that some important theoretical aspects of BVP with transmission conditions were studied in [3,4,[9][10][11][12][13] and corresponding references cited therein.…”