Showing papers by "Patricia J. Y. Wong published in 2022"
TL;DR: In this paper , a numerical scheme based on a general temporal mesh is constructed for a generalized time fractional diffusion problem of order α. The main idea involves the generalized linear interpolation and so they term the numerical scheme the gL1 scheme.
Abstract: In this paper, a numerical scheme based on a general temporal mesh is constructed for a generalized time-fractional diffusion problem of order α. The main idea involves the generalized linear interpolation and so we term the numerical scheme the gL1 scheme. The stability and convergence of the numerical scheme are analyzed using the energy method. It is proven that the temporal convergence order is (2−α) for a general temporal mesh. Simulation is carried out to verify the efficiency of the proposed numerical scheme.
4 citations
11 Dec 2022
TL;DR: In this paper , a high order approximation for generalized Caputo fractional derivative of order α in 0,1 was proposed, which is shown to be O(tau^{3-α)-approximation.
Abstract: In this paper, we propose a high order approximation for generalized Caputo fractional derivative of order $\alpha\in(0,1)$. The approximation order is shown to be $O(\tau^{3-\alpha})$ which improves some previous work done to date. We then apply the new approximation to solve a class of generalized time fractional sub-diffusion problem. Some experiments are carried out to demonstrate the accuracy of the proposed methods. The numerical results indicate consistency with the theoretical results and good performance of the methods.
TL;DR: In this article , a Legendre wavelet collocation method is proposed for solving a nonlinear coupled time fractional diffusion system, which is quasi-linearized by making use of the Newton's method.
Abstract: A Legendre wavelet collocation method is proposed for solving a nonlinear coupled time fractional diffusion system. We have formulated a Riemann-Liouville fractional integral operator for Legendre wavelet (RLFIO-L) adopting the definition of Riemann-Liouville fractional integral operator combined with the Laplace transformation. Both the time and space variables are discretized in terms of the Legendre wavelet and RLFIO-L. The nonlinear coupled diffusion system is quasi-linearized by making use of the Newton's method. For theoretical concerns, the upper bound of error norm of the proposed method is estimated. Some numerical experiments are presented to authenticate the computational efficacy of the method.