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Sylvester Equations and the numerical solution of partial fractional differential equations.
- Source :
-
Journal of Computational Physics . Jul2015, Vol. 293, p370-384. 15p. - Publication Year :
- 2015
-
Abstract
- We develop a new matrix-based approach to the numerical solution of partial differential equations (PDE) and apply it to the numerical solution of partial fractional differential equations (PFDE). The proposed method is to discretize a given PFDE as a Sylvester Equation, and parameterize the integral surface using matrix algebra. The combination of these two notions results in an algorithm which can solve a general class of PFDE efficiently and accurately by means of an O ( n 3 ) algorithm for solving the Sylvester Matrix Equation (over an m × n grid with m ∼ n ). The proposed parametrization of the integral surface allows for the solution with the more general Robin boundary conditions, and allows for high-order approximations to derivative boundary conditions. To achieve our ends, we also develop a new matrix-based approximation to fractional order derivatives. The proposed method is demonstrated by the numerical solution of the fractional diffusion equation with fractional derivatives in both the temporal and spatial directions. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00219991
- Volume :
- 293
- Database :
- Academic Search Index
- Journal :
- Journal of Computational Physics
- Publication Type :
- Academic Journal
- Accession number :
- 102494906
- Full Text :
- https://doi.org/10.1016/j.jcp.2014.12.033