Work

Petrov-Galerkin Method for Fully Distributed-Order Fractional Partial Differential Equations

Year: 2018

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1805.08242

Authors: Samiee, Mehdi, Kharazmi, Ehsan, Zayernouri, Mohsen, Meerschaert, Mark M

Institution: Michigan State University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Multidisciplinary University Research Initiative, Air Force Office of Scientific Research, Army Research Office

Awards: G1072749480, G1523888516, G260750634, G3036909949, G3552121337, G3855399100, G4420234770, FRG: Collaborative Research: Extreme Value Theory for Spatially Indexed Functional Data, G4946931266, G5385673730, INSPIRE Track 1: Earthcasting fluvial systems: Physical, ecological, and biogeochemical dynamics, G7142813775, G7358895889, G7452299184, G8257659198

OpenAlex ID: W2804123559

Cites: 24

Cited by: 12

Related to: 10