 In this paper, we propose a numerical method to solve initial boundary value problems, IBVP, of Laplace partial differential equations, PDE. We use finite difference methods to approximate the solutions and ensure their stability. To test the accuracy of our method, we provide two examples of initial boundary value problems and compare the numerical solution with the exact solution. Our results show that the proposed method provides accurate and reliable solutions. Furthermore, we implement MATLAB software to calculate the absolute error between the numerical and exact solutions. Finally, we present illustrative graphs to demonstrate the accuracy of the proposed method. This article was authored by Bawur Muhammad Faraj, Dana Taha Muhammad Sali, Nar Hamma Zaman Hamma Ali, and others.