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BIT Numerical Mathematics
Erschienen in: BIT Numerical Mathematics 4/2015

01.12.2015

A compact finite difference method for solving a class of time fractional convection-subdiffusion equations

verfasst von: Yuan-Ming Wang

Erschienen in: BIT Numerical Mathematics | Ausgabe 4/2015

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Abstract

A high-order compact finite difference method is proposed for solving a class of time fractional convection-subdiffusion equations. The convection coefficient in the equation may be spatially variable, and the time fractional derivative is in the Caputo’s sense with the order \(\alpha \) (\(0<\alpha <1\)). After a transformation of the original equation, the spatial derivative is discretized by a fourth-order compact finite difference method and the time fractional derivative is approximated by a \((2-\alpha )\)-order implicit scheme. The local truncation error and the solvability of the method are discussed in detail. A rigorous theoretical analysis of the stability and convergence is carried out using the discrete energy method, and the optimal error estimates in the discrete \(H^{1}\), \(L^{2}\) and \(L^{\infty }\) norms are obtained. Applications using several model problems give numerical results that demonstrate the effectiveness and the accuracy of this new method.
Vorheriger Artikel An optimal a priori error estimate in the maximum norm for the Il’in scheme in 2D
Nächster Artikel Faster SDC convergence on non-equidistant grids by DIRK sweeps

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Metadaten
Titel
A compact finite difference method for solving a class of time fractional convection-subdiffusion equations
verfasst von
Yuan-Ming Wang
Publikationsdatum
01.12.2015
Verlag
Springer Netherlands
Erschienen in
BIT Numerical Mathematics / Ausgabe 4/2015
Print ISSN: 0006-3835
Elektronische ISSN: 1572-9125
DOI
https://doi.org/10.1007/s10543-014-0532-y

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