Search

Your search keyword '"Zhang, Jia-Li"' showing total 2 results
Start Over Author "Zhang, Jia-Li" Topic caputo fractional derivatives
2 results on '"Zhang, Jia-Li"'

1. An [formula omitted]-robust fast algorithm for distributed-order time–space fractional diffusion equation with weakly singular solution.

Author

Sun, Lu-Yao, Lei, Siu-Long, Sun, Hai-Wei, and Zhang, Jia-Li

Subjects
*GAUSSIAN quadrature formulas, *CONJUGATE gradient methods, *FINITE difference method, *CAPUTO fractional derivatives, *DIRECTIONAL derivatives, *DISTRIBUTED algorithms, *HEAT equation, *DISCRETE wavelet transforms
Abstract

A fast algorithm is proposed for solving two-dimensional distributed-order time–space fractional diffusion equation where the solution has a weak singularity at initial time. The distributed-order fractional problem is firstly transformed into multi-term fractional problem by the Gauss–Legendre quadrature formula. Then the exponential-sum-approximation method on graded mesh is utilized to discretize time Caputo fractional derivatives in time direction, and a standard finite difference method is employed to approximate the spatial Riesz fractional derivatives. The scheme is proved to be α -robust convergent analytically. The discrete linear system possesses symmetric positive definite block-Toeplitz–Toeplitz-block structure and is efficiently solved by conjugate gradient method with the state-of-the-art sine-transformed based preconditioner. Numerical examples confirm the error analysis and the effectiveness of the preconditioner. [ABSTRACT FROM AUTHOR]

Published
2023
Full Text
View/download PDF

2. A fast algorithm for two-dimensional distributed-order time-space fractional diffusion equations.

Author

Sun, Lu-Yao, Fang, Zhi-Wei, Lei, Siu-Long, Sun, Hai-Wei, and Zhang, Jia-Li

Subjects
*GAUSSIAN quadrature formulas, *DISTRIBUTED algorithms, *CONJUGATE gradient methods, *FINITE difference method, *CAPUTO fractional derivatives, *FINITE differences, *HEAT equation, *ALGORITHMS
Abstract

• Two-dimensional distributed-order time-space fractional diffusion problem is considered and its finite difference discretization is studied. • The stability and convergence of the scheme are investigated. • The spatial second-order convergence and the temporal optimal convergence are obtained. • A fast and memory saving algorithm for solving DO time-space fractional diffusion equation is developed through Gauss quadrature formula, ESA method and PCG method. • Numerical experiments show strong effectiveness and efficiency of the method. In this paper, a fast algorithm is proposed for solving distributed-order time-space fractional diffusion equations. Integral terms in time and space directions are discretized by the Gauss-Legendre quadrature formula. The Caputo fractional derivatives are approximated by the exponential-sum-approximation method, and the finite difference method is applied for spatial approximation. The coefficient matrix of the discretized linear system is symmetric positive definite and possesses block-Toeplitz-Toeplitz-block structure. The preconditioned conjugate gradient method with a block-circulant-circulant-block preconditioner is employed to solve the linear system. Theoretically, the stability and convergence of the proposed scheme are discussed. Numerical experiments are carried out to demonstrate the effectiveness of the scheme. [ABSTRACT FROM AUTHOR]

Published
2022
Full Text
View/download PDF

Catalog

Books, media, physical & digital resources
See catalog results