Bibliographic Details
| Title: |
IRK-WSGD methods for space fractional diffusion equations. |
| Authors: |
Lin, Fu-Rong1 (AUTHOR) frlin@stu.edu.cn, Qiu, Yi-Feng1 (AUTHOR), She, Zi-Hang1,2 (AUTHOR) |
| Source: |
Applied Numerical Mathematics. Jun2021, Vol. 164, p222-244. 23p. |
| Subjects: |
Heat equation, Initial value problems, Ordinary differential equations, Linear systems |
| Abstract: |
In this paper, we develop high order numerical schemes for the solution of the initial-boundary value problem of one-dimensional and two-dimensional space fractional diffusion equations of orders belonging to the interval (1 , 2). Firstly, certain weighted and shifted Grünwald difference (WSGD) operator is used to approximate space Riemann-Liouville fractional derivatives, resulting in a linear system of ordinary differential equations (ODEs). Then an implicit Runge-Kutta (IRK) method is applied to discretize the resulted ODEs. Thus, we get an IRK-WSGD method for the fractional diffusion equation. We prove that under certain hypotheses, the proposed IRK-WSGD schemes are stable and have temporally fourth order accuracy and spatially second/third order accuracy. Preconditioning for discretization linear systems is discussed. Numerical experiments are presented to illustrate the accuracy and efficiency of the method. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
