Rational approximation to the fractional Laplacian operator in reaction-diffusion problems
Numerical Analysis
2024-03-19 v1
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.
Cite
@article{arxiv.1607.04166,
title = {Rational approximation to the fractional Laplacian operator in reaction-diffusion problems},
author = {Lidia Aceto and Paolo Novati},
journal= {arXiv preprint arXiv:1607.04166},
year = {2024}
}