• ### A Validation for Dirichlet Problem

Ummu Sahin Sener1, Ersin Sener2*

1. Department of Mathematics, Kirklareli University, Kayali Campus, 39000, Kirklareli, Turkey.
2. Department of Mathematics, Yildiz Technical University, Esenler, 34220, Istanbul, Turkey.

Abstract: Euler method is often referred method because of ease of use and usefulness for ordinary differential equation. Usefulness is arises from simplicity and error analyses comfortableness. It is convenient for a second order differential equation because of reducibility. It is also used for Dirichlet problem. Analytical solution is compared with numerical approach. Analytical solution, numerical approach and error analyses are together reconfigured. Analytical solution is done Evolutionary Approach to Electromagnetics’ frame. Despite the fact that the approach is to be required solution of Klein-Gordon equation, it is just validated with 0.02 step Dirichlet problems’ numerical approach and analytical solution.

Keywords: Dirichlet boundary-value problem, analytical solution, numerical solution, Maxwell equations, TM time-domain mode.