Study of Higher Order Numerical Methods for Solving Parabolic Partial Differential Equations with Applications

Abstract

Parabolic Partial Differential equations have clearly emerged in many branches of science, for example technology, engineering, physics and many others. So based on the importance of parabolic equations, new efficient and more accurate numerical methods were discussed, studied and analyzed. These numerical methods are Explicit Method, Implicit Method, Crank-Nicolson Method, Finite Difference Method, Method of Line, And Pade Approximation. Each method has been studied and implemented with examples and A MATLAB code was written for each method to obtain very accurate results. The Numerical results were compared to determine the best method which is the most accurate