Analisis Numerik dalam Pemecahan Persamaan Diferensial Parsial

Abstract

Partial Differential Equations (PDEs) are widely used in various fields of science, such as physics, engineering, and finance, to model complex phenomena such as heat transfer, fluid dynamics, and wave propagation. However, analytical solutions to PDEs are often difficult or even impossible to obtain, making numerical approaches necessary. This study aims to analyze numerical methods for solving PDEs, with a focus on the finite difference and finite element methods. We compare the accuracy, stability, and computational efficiency of various numerical schemes using MATLAB-based simulations. The results indicate that the finite element method performs better in handling complex geometries, while the finite difference method is more efficient for computations on uniform domains. With the appropriate method selection, numerical approaches can be effectively used to solve various problems modeled by PDEs. This study is expected to provide insights for the development of more accurate and efficient numerical methods in a wide range of scientific and engineering applications.