Journal of Studies in Science and Engineering Journal of Studies in Science and Engineering. 2022, 2(4), 50-59. https://doi.org/10.53898/josse2022245 https://engiscience.com/index.php/josse Research Article On the Numerical Solution for Two Dimensional Laplace Equation with Initial Boundary Conditions by using Finite Difference Methods Bawar Mohammed Faraj 1,* , Dana Taha Mohammed Salih 1 , Bnar Hama Zaman Hama Ali 2 , Bahadin Muhammad Hussien 2 , Sarkhel Akbar Mahmood 2 , Shewa Abid Hama 2 1 Computer Science Department of Physics, College of Science, University of Halabja, Halabja, 46018, Iraq 2 Department of Physics, College of Science, University of Halabja, Halabja, 46018, Iraq *Corresponding Author: Bawar Mohammed Faraj, E-mail: bawarm.faraj@uoh.edu.iq Article Info Abstract Article History Received Nov 28,2022 Revised Dec 24, 2022 Accepted Dec 27, 2022 In this study, Laplace partial differential equations with initial boundary conditions has been studied. A numerical method has been proposed for the solution of the IBVP Laplace equation. The technique based on finite difference methods. The stability of the difference schemes are guaranteed. Approximation solution of the problem was achieved. For testing the accuracy of the proposed method, two different initial boundary value problems are provided. Moreover, a com- parison between the numerical solution and analytical solution has been done. MATLAB soft- ware implemented for calculation of absolute errors. Illustration graphs presented. It has been demonstrated that the results of the comparison guarantee the accuracy and reliability of the pro- vided method. Keywords Laplace equation IBVP Error analysis Approximation Solution Finite difference method Copyright: © 2022 Bawar Mohammed Faraj, Dana Taha Mohammed Salih, Bnar Hama Zaman Hama Ali, Bahadin Muhammad Hussien, Sarkhel Akbar Mahmood and Shewa Abid Hama. This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY 4.0) license. 1. Introduction Recently, Differential Equations (DE) have been the focus of a lot of studies [1, 2]. DE is important for modeling various problems such as electrodynamics, elasticity, wave propagation, signal analysis, and thermodynamics [3-5]. Differential equations have been applied for many problems in science, engineering, finance, physics and seismology[1, 6-9]. Many methods for the exact solution have been presented for solving Differential equations[10-14]. Although the exact solution of some types of DE can be found [1-3, 5]., many numerical methods have been applied for solving linear and non-linear differential equations [15, 16]. In the case of Partial differential equations, much attention has been given in the works to test the reliability and accuracy of the approximation and numerical techniques [17]. Many researchers applied finite difference approximations for numerical solution of different kinds of PDE’s in works [7, 18-25].