Search

In this paper, the formulation of a new fractional modified explicit group (FMEG) iterative method in solving the two-dimensional time fractional diffusion equation (TFDE) is presented. The method is formulated using the fivepoint centred difference approximation on the 2h grid stencils. The new developed method is shown to have a better convergence rate due to its lower computational complexity compared to others existing fractional group methods. Numerical experimentations of this new method, show significant improvement in execution time over the other explicit methods of the same class which enhances the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In order to improve the accuracy of solutions of partial differential equations (PDEs), the formulation of higher order solvers may be inevitable. In this paper, we propose a new fourth-order finite difference scheme derived from the nine-point approximation formula on the rotated grid in solving the two-dimensional Poisson PDE with Dirichlet boundary conditions. Several numerical experiments are carried out and the results are compared with the analytical solutions to verify the higher accuracy of the presented schemes. [ABSTRACT FROM AUTHOR]