Alternating Direction Implicit Method for Solving Parabolic Partial Differential Equations in Three Dimensions

Abstract

In this paper, the parabolic partial differential equations in three-dimensions are solved by two types of finite differences, such as, Alternating Direction Explicit (ADE) method and Alternating Direction Implicit (ADI) method. By the comparison of the numerical results for the previous two methods with the Exact solution, we observe that the results of Alternating Direction Implicit (ADI) method is better and nearest to the exact solution compared with the results of Alternating Direction Explicit (ADE) method. we also studied the numerical stability of both methods by Von-Neumann Method.

Keywords

• parabolic partial differential equations in three dimensions
• finite difference methods
• alternating direction explicit method
• alternating direction implicit method
• von-neumann method