Modified FDM for Solving Two-linked Boundary-value Problems with Transmission Conditions

Abstract

In this paper, numerical solutions of boundary value problems (BVPs) for twolinked ordinary differential equations (ODEs) is discussed. The problem studied here differs from classical BVPs in that it includes additional conditions at the point of interaction, called transmission conditions.
We developed a new numerical method for calculating the numerical solution of BVTPs for two-linked ODEs based on the finite difference method (FDM), and to demonstrate the reliability and efficiency of the method, the obtained numerical solutions were graphically compared with the corresponding exact solutions. We also illustrated the convergence of the method using maximum absolute error (MAE) and the results are shown in the tables.