Back to Search
Start Over
Preconditioned quasi-compact boundary value methods for space-fractional diffusion equations
- Source :
- Numerical Algorithms. 84:633-649
- Publication Year :
- 2019
- Publisher :
- Springer Science and Business Media LLC, 2019.
-
Abstract
- This paper focuses on highly efficient numerical methods for solving space-fractional diffusion equations. By combining the fourth-order quasi-compact difference scheme and boundary value methods, a class of quasi-compact boundary value methods are constructed. In order to accelerate the convergence rate of this class of methods, the Kronecker product splitting (KPS) iteration method and the preconditioned method with KPS preconditioner are proposed. A convergence criterion for the KPS iteration method is derived. A numerical experiment further illustrates the computational efficiency and accuracy of the proposed methods. Moreover, a numerical comparison with the preconditioned method with Strang-type preconditioner is given, which shows that the preconditioned method with KPS preconditioner is comparable in computational efficiency.
- Subjects :
- Kronecker product
Preconditioner
Iterative method
Applied Mathematics
Numerical analysis
Space-fractional diffusion equations, Quasi-compact difference scheme, Boundary value methods, KPS preconditioner, Preconditioned methods
010103 numerical & computational mathematics
Computer Science::Numerical Analysis
01 natural sciences
Mathematics::Numerical Analysis
010101 applied mathematics
symbols.namesake
Rate of convergence
Theory of computation
Convergence (routing)
symbols
Applied mathematics
0101 mathematics
Diffusion (business)
Mathematics
Subjects
Details
- ISSN :
- 15729265 and 10171398
- Volume :
- 84
- Database :
- OpenAIRE
- Journal :
- Numerical Algorithms
- Accession number :
- edsair.doi.dedup.....f65643cbcb6fee876bd452d2e3db9621