Rational Approximation to the Fractional Laplacian Operator in Reaction-Diffusion Problems

Abstract

This paper provides a new numerical strategy for solving fractional-in-space reaction-diffusion equations on bounded domains under homogeneous Dirichlet boundary conditions. Using the matrix transfer technique 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 semilinear initial value problem in which the matrices involved are sparse. Numerical results are presented to verify the effectiveness of the proposed solution strategy.