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Investigating the Efficiency of Numerical Methods in Solving Partial Differential Equations

Introduction Partial Differential Equations (PDEs) play a fundamental role in mathematical modeling of physical phenomena in various disciplines, including physics, engineering, and finance. Solving these equations analytically is often challenging or even impossible, leading to the need for numerical methods. In recent years, researchers have focused on developing efficient algorithms to solve PDEs numerically. This article aims to investigate the efficiency of numerical methods in solving PDEs by analyzing the classic and new trends in computation and algorithms.