This paper provides a new numerical strategy to solve fractional in space reaction-diffusion equations on a bounded domain under homogeneous Dirichlet boundary conditions. Using the matrix transform method the fractional Laplacian operator is replaced by a matrix which, in general, is dense. The approach here presented is based on the approximation of this matrix by the product of two suitable banded matrices. This leads to a semi-linear initial value problem in which the matrices involved are sparse. Numerical results are presented to verify the effectiveness of the proposed solution strategy.
Rational approximation to the fractional laplacian operator in reaction-diffusion problems
NOVATI, PAOLO
2017-01-01
Abstract
This paper provides a new numerical strategy to solve fractional in space reaction-diffusion equations on a bounded domain under homogeneous Dirichlet boundary conditions. Using the matrix transform method the fractional Laplacian operator is replaced by a matrix which, in general, is dense. The approach here presented is based on the approximation of this matrix by the product of two suitable banded matrices. This leads to a semi-linear initial value problem in which the matrices involved are sparse. Numerical results are presented to verify the effectiveness of the proposed solution strategy.File | Dimensione | Formato | |
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