Bernstein dual-Petrov-Galerkin method: application to 2D time fractional diffusion equation

Abstract

In this paper, we develop a Bernstein dual-Petrov-Galerkin method for the numerical simulation of a two-dimensional fractional diffusion equation. A spectral discretization is applied by introducing suitable combinations of dual Bernstein polynomials as the test functions and the Bernstein polynomials as the trial ones. We derive the exact sparse operational matrix of differentiation for the dual Bernstein basis which provides a matrix based approach for the spatial discretization. It is shown that the method leads to banded linear systems that can be solved efficiently. The stability and convergence of the proposed method is discussed. Finally, some numerical examples are provided to support the theoretical claims and to show the accuracy and efficiency of the method.

arXiv comment18 pages, Accepted for publication in Computational and Applied Mathematics (Springer)

References in corpus (5)

• Viscoelastic subdiffusion: from anomalous to normal
• Bézier representation of the constrained dual Bernstein polynomials
• Efficient numerical solution of the time fractional diffusion equation by mapping from its Brownian counterpart
• A numerical scheme for space-time fractional advection-dispersion equation
• Banded operational matrices for Bernstein polynomials and application to the fractional advection-dispersion equation

Cited by in corpus (1)

• Bernstein modal basis: application to the spectral Petrov-Galerkin method for fractional partial differential equations