Showing papers by "Patricia J. Y. Wong published in 2018"
12 citations
10 citations
TL;DR: This paper proposes a numerical scheme and rigorously proves its solvability, convergence and stability in maximum norm, and shows that the theoretical convergence order improves those of earlier work.
10 citations
01 Nov 2018
TL;DR: A quintic non-polynomial spline approach coupled with $L1$ formula for the numerical treatment of time-fractional nonlinear Schrödinger equation and the unconditional stability is proved by Fourier method.
Abstract: In this paper, we propose a quintic non-polynomial spline approach coupled with $L1$ formula for the numerical treatment of time-fractional nonlinear Schrodinger equation. The unconditional stability is proved by Fourier method for $0 , where $\gamma$ is the order of the Caputo time-fractional derivative. The efficiency of the proposed numerical scheme is illustrated by numerical experiments, where the simulation results indicate better performance over previous work in the literature.
6 citations
TL;DR: In this article, a mid-knot cubic non-polynomial spline is applied to obtain the numerical solution of a system of second-order boundary value problems, which is proved to be uniquely solvable and it is of secondorder accuracy.
Abstract: In this paper, a mid-knot cubic non-polynomial spline is applied to obtain the numerical solution of a system of second-order boundary value problems. The numerical method is proved to be uniquely solvable and it is of second-order accuracy. We further include three examples to illustrate the accuracy of our method and to compare with other methods in the literature.
4 citations
01 Jul 2018
1 citations
01 Nov 2018
TL;DR: It is shown that the numerical scheme is stable and convergent and the theoretical convergence order improves those of earlier work.
Abstract: In this paper, we tackle the numerical treatment of a fourth-order fractional diffusion-wave problem using parametric quintic spline. It is shown that the numerical scheme is stable and convergent and the theoretical convergence order improves those of earlier work. To confirm, simulation is carried out to demonstrate its efficiency.
TL;DR: In this paper, a new method to convert boundary value problems for impulsive fractional differential equations involving Caputo fractional derivatives to integral equations is presented, which relies on the well known Schauder's fixed point theorem.
Abstract: We present a new method to convert the boundary value problems for impulsive fractional differential equations involving Caputo fractional derivatives to integral equations. This method is used to solve a classes of boundary value problems for impulsive fractional differential equations. Moreover, some new results on the existence of solutions of anti-periodic boundary value problems for impulsive fractional differential systems are established (see Sect. 3). Our analysis relies on the well known Schauder’s fixed point theorem. Some examples and comments on recent published papers are given to illustrate the differences between our main theorems and known results.
10 Jul 2018
TL;DR: In this article, a generalized L 1 − 2 formula for new generalized fractional Caputo derivatives was developed and theoretically shown that this new approximation achieves O(τ3−α) (τ is the step size) which improves earlier work done to date.
Abstract: In this paper, we shall develop a generalized L1 − 2 formula for new generalized fractional Caputo derivatives. It is theoretically shown that this new approximation achieves O(τ3−α) (τ is the step size) which improves earlier work done to date. Also, numerical tests and an application are presented to demonstrate the efficiency and accuracy of the proposed method.
10 Jul 2018
TL;DR: In this paper, a new numerical scheme for fourth-order fractional diffusion wave model is proposed and the solvability, stability and convergence of proposed method are established in l 2 norm and it is shown that the numerical scheme improves the earlier work done.
Abstract: In this paper, we shall construct a new numerical scheme for fourth-order fractional diffusion wave model. The solvability, stability and convergence of proposed method are established in l2 norm and it is shown that the numerical scheme improves the earlier work done. Simulation is carried out to verity the accuracy and efficiency of the numerical scheme.