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- Title
Bernstein modal basis: Application to the spectral Petrov-Galerkin method for fractional partial differential equations.
- Authors
Jani, M.; Babolian, E.; Javadi, S.
- Abstract
In the spectral Petrov-Galerkin methods, the trial and test functions are required to satisfy particular boundary conditions. By a suitable linear combination of orthogonal polynomials, a basis, that is called the modal basis, is obtained. In this paper, we extend this idea to the nonorthogonal dual Bernstein polynomials. A compact general formula is derived for the modal basis functions based on dual Bernstein polynomials. Then, we present a Bernstein-spectral Petrov-Galerkin method for a class of time fractional partial differential equations with Caputo derivative. It is shown that the method leads to banded sparse linear systems for problems with constant coefficients. Some numerical examples are provided to show the efficiency and the spectral accuracy of the method.
- Subjects
AMBER; GALERKIN methods; ORTHOGONAL polynomials; CAPUTO fractional derivatives; MODAL models
- Publication
Mathematical Methods in the Applied Sciences, 2017, Vol 40, Issue 18, p7663
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.4551