Least squares finite-element solution of a fractional order two-point boundary value problem

By George J. Fix III, J. Roof. 2004

235 citations recorded by the source corpus.

Subfields: Mechanics of Materials, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/f3f7e4121af1cbabec17dbca5c7d5551568fd83a

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In Mechanics of Materials

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Variational formulation for the stationary fractional advection dispersion equation (2006, methodology): “Aside from [5] we are not aware of any other papers in the literature which investigate the Galerkin approximation and associated error analysis for the FADE.”
A second-order accurate numerical approximation for the fractional diffusion equation (2006, methodology): “Several different first-order accurate numerical methods to solve fractional diffusion equations have been presented before [3,4,6,7,9,10].”
A unified Petrov-Galerkin spectral method for fractional PDEs (2015, methodology): “[31] G.J. Fix, J.P. Roop, Least squares finite-element solution of a fractional order two-point boundary value problem, Comput.”
Implicit difference approximation for the time fractional diffusion equation (2006, methodology): “Fix and Roop [ 4 ] developed a finite element method for a two-point boundary value problem.”
A VARIATIONAL APPROACH FOR A PROBLEM INVOLVING A ψ-HILFER FRACTIONAL OPERATOR (2021, background): “We also quote the references [5,7,11,14,16,17,22,25,26,32,35,43,46] Let Ω ⊂ R (N ≥ 2) be a bounded domain with smooth boundary.”
Finite difference methods for two-dimensional fractional dispersion equation (2006, methodology): “Ervin and Roop [14] extend this approach for multi-dimensional partial differential equations with constant coefficients on the fractional derivative terms.”
An application of fractional differential equations to risk theory (2019, background): “For other applications, we refer to [19, 22, 29, 40] and the references therein.”
Variational solution of fractional advection dispersion equations on bounded domains in ℝd (2007, methodology): “8 [5] [Fractional Poincaré-Friedrichs] For u ∈ J L(I), we have ‖u‖L2(I) ≤ C|u|Jμ L(I), (A.”