Affiliation:
1. College of Mathematical Sciences , Yangzhou University , Yangzhou 225002 , China
2. Faculty of Education , University of Khartoum , Khartoum P. O. Box 321 , Sudan
Abstract
Abstract
This paper presents a linearized finite difference scheme for solving a kind of time-space fractional nonlinear diffusion-wave equations with initial singularity, where the Caputo fractional derivative in time and the Riesz fractional derivative in space are involved. First, the considered problem is equivalently transformed into its partial integro-differential form. Then, the fully discrete scheme is constructed by using the Crank–Nicolson technique, the L1 approximation, and the convolution quadrature formula to deal with the temporal discretizations. Meanwhile, the classical central difference formula and the fractional central difference formula are applied to approximate the second-order derivative and the Riesz fractional derivative in space, respectively. Moreover, the stability and convergence of the proposed scheme are strictly proved by using the discrete energy method. Finally, some numerical experiments are presented to illustrate the theoretical results.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Jiangsu Province of China
Subject
Applied Mathematics,General Physics and Astronomy,Mechanics of Materials,Engineering (miscellaneous),Modeling and Simulation,Computational Mechanics,Statistical and Nonlinear Physics