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Journal of Scientific Computing

Erschienen in:

18.03.2015

An ADI Crank–Nicolson Orthogonal Spline Collocation Method for the Two-Dimensional Fractional Diffusion-Wave Equation

verfasst von: Graeme Fairweather, Xuehua Yang, Da Xu, Haixiang Zhang

Erschienen in: Journal of Scientific Computing | Ausgabe 3/2015

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Abstract

A new method is formulated and analyzed for the approximate solution of a two-dimensional time-fractional diffusion-wave equation. In this method, orthogonal spline collocation is used for the spatial discretization and, for the time-stepping, a novel alternating direction implicit method based on the Crank–Nicolson method combined with the \(L1\)-approximation of the time Caputo derivative of order \(\alpha \in (1,2)\). It is proved that this scheme is stable, and of optimal accuracy in various norms. Numerical experiments demonstrate the predicted global convergence rates and also superconvergence.

Vorheriger Artikel Simple Finite Element Numerical Simulation of Incompressible Flow Over Non-rectangular Domains and the Super-Convergence Analysis

Nächster Artikel A Kansa-Radial Basis Function Method for Elliptic Boundary Value Problems in Annular Domains

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Titel: An ADI Crank–Nicolson Orthogonal Spline Collocation Method for the Two-Dimensional Fractional Diffusion-Wave Equation
verfasst von: Graeme Fairweather
Xuehua Yang
Da Xu
Haixiang Zhang
Publikationsdatum: 18.03.2015
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 3/2015
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-015-0003-x

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