Fractional Group Iterative Methods For Two Dimensional Time-Fractional Differential Equations - Balasim, Alla Tareq (2017)
Fractional partial differential equations (FPDEs) are highly effective and powerful tools for modeling problems in engineering, physics, and other fields because of their non-local properties. Most FPDEs can not solved analytically. Therefore, developing accurate, efficient, stable, and easy-to-implement methods is an important task. To date, ample numerical methods have been proposed for solving the time and/or space FPDEs, such as the finite difference and finite element methods. A large and sparse system of linear equations will arise when FPDEs are discretised using certain discretisation schemes based on finite element or finite difference methods which requires a considerable amount of execution time since earlier solutions have to be saved if the current solution is to be computed. This thesis focuses on the development of new, accurate, efficient, and fast numerical methods for solving FPDEs.