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Journal of Scientific Computing
Erschienen in: Journal of Scientific Computing 2/2017

11.02.2017

A Two-Grid Block-Centered Finite Difference Method for the Nonlinear Time-Fractional Parabolic Equation

verfasst von: Xiaoli Li, Hongxing Rui

Erschienen in: Journal of Scientific Computing | Ausgabe 2/2017

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Abstract

In this article, a two-grid block-centered finite difference scheme is introduced and analyzed to solve the nonlinear time-fractional parabolic equation. This method is considered where the nonlinear problem is solved only on a coarse grid of size H and a linear problem is solved on a fine grid of size h. Stability results are proven rigorously. Error estimates are established on non-uniform rectangular grid which show that the discrete \(L^{\infty }(L^2)\) and \(L^2(H^1)\) errors are \(O(\triangle t^{2-\alpha }+h^2+H^3)\). Finally, some numerical experiments are presented to show the efficiency of the two-grid method and verify that the convergence rates are in agreement with the theoretical analysis.
Vorheriger Artikel Optimized Overlapping Schwarz Waveform Relaxation for a Class of Time-Fractional Diffusion Problems
Nächster Artikel Unconditionally Optimal Error Analysis of Crank–Nicolson Galerkin FEMs for a Strongly Nonlinear Parabolic System

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Metadaten
Titel
A Two-Grid Block-Centered Finite Difference Method for the Nonlinear Time-Fractional Parabolic Equation
verfasst von
Xiaoli Li
Hongxing Rui
Publikationsdatum
11.02.2017
Verlag
Springer US
Erschienen in
Journal of Scientific Computing / Ausgabe 2/2017
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-017-0380-4

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