Petrov-Galerkin Method for Fully Distributed-Order Fractional Partial Differential Equations
Numerical Analysis
2018-05-23 v1
Abstract
Distributed-order PDEs are tractable mathematical models for complex multiscaling anomalous transport, where derivative orders are distributed over a range of values. We develop a fast and stable Petrov-Galerkin spectral method for such models by employing Jacobi \textit{poly-fractonomial}s and Legendre polynomials as temporal and spatial basis/test functions, respectively. By defining the proper underlying \textit{ distributed Sobolev} spaces and their equivalent norms, we prove the well-posedness of the weak formulation, and thereby carry out the corresponding stability and error analysis. We finally provide several numerical simulations to study the performance and convergence of proposed scheme.
Cite
@article{arxiv.1805.08242,
title = {Petrov-Galerkin Method for Fully Distributed-Order Fractional Partial Differential Equations},
author = {Mehdi Samiee and Ehsan Kharazmi and Mohsen Zayernouri and Mark M Meerschaert},
journal= {arXiv preprint arXiv:1805.08242},
year = {2018}
}