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arXiv · 1607.04166

Rational approximation to the fractional Laplacian operator in reaction-diffusion problems

Lidia Aceto·Paolo Novati
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Abstract

This paper provides a new numerical strategy to solve fractional in space reaction-diffusion equations on bounded domains 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.

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Lidia Aceto, Paolo Novati. 2016-07-14. Rational approximation to the fractional Laplacian operator in reaction-diffusion problems. https://doi.org/10.1137/16m1064714

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