article

Two finite difference schemes for time fractional diffusion-wave equation

Authors:

Jiye YangAuthors Info & Claims

Numerical Algorithms, Volume 64, Issue 4

Pages 707 - 720

https://doi.org/10.1007/s11075-012-9689-0

Published: 01 December 2013 Publication History

Abstract

Time fractional diffusion-wave equations are generalizations of classical diffusion and wave equations which are used in modeling practical phenomena of diffusion and wave in fluid flow, oil strata and others. In this paper we construct two finite difference schemes to solve a class of initial-boundary value time fractional diffusion-wave equations based on its equivalent partial integro-differential equations. Under the weak smoothness conditions, we prove that our two schemes are convergent with first-order accuracy in temporal direction and second-order accuracy in spatial direction. Numerical experiments are carried out to demonstrate the theoretical analysis.

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Two finite difference schemes for time fractional diffusion-wave equation
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
    2. Numerical analysis
2. Theory of computation

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cover image Numerical Algorithms

Numerical Algorithms Volume 64, Issue 4

December 2013

161 pages

ISSN:1017-1398

Issue’s Table of Contents

Copyright © Copyright © 2013 Springer Science+Business Media New York.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 December 2013

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Cited By

Tan Z(2025)Second-order non-uniform and fast two-grid finite element methods for non-linear time-fractional mobile/immobile equations with weak regularityApplied Mathematics and Computation10.1016/j.amc.2024.129043486:COnline publication date: 1-Feb-2025
https://dl.acm.org/doi/10.1016/j.amc.2024.129043
Yang JLi YLiu Z(2024)A finite difference/Kansa method for the two-dimensional time and space fractional Bloch-Torrey equationComputers & Mathematics with Applications10.1016/j.camwa.2023.12.007156:C(1-15)Online publication date: 15-Feb-2024
https://dl.acm.org/doi/10.1016/j.camwa.2023.12.007
Tan ZZeng Y(2024)Temporal second-order fully discrete two-grid methods for nonlinear time-fractional variable coefficient diffusion-wave equationsApplied Mathematics and Computation10.1016/j.amc.2023.128457466:COnline publication date: 1-Apr-2024
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Jia JJiang XChi X(2024)Improved uniform error bounds of Lawson-type exponential integrator method for long-time dynamics of the high-dimensional space fractional sine-Gordon equationNumerical Algorithms10.1007/s11075-023-01745-097:3(1179-1214)Online publication date: 1-Nov-2024
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Luo YWei T(2024)Uniqueness and Numerical Method for Determining a Spatial Source Term in a Time-Fractional Diffusion Wave EquationJournal of Scientific Computing10.1007/s10915-024-02523-399:2Online publication date: 10-Apr-2024
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Cui M(2023)An alternating direction implicit compact finite difference scheme for the multi-term time-fractional mixed diffusion and diffusion–wave equationMathematics and Computers in Simulation10.1016/j.matcom.2023.06.003213:C(194-210)Online publication date: 1-Nov-2023
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Othmani STatar N(2023)Well‐posedness and Mittag–Leffler stability for a nonlinear fractional telegraph problemAsian Journal of Control10.1002/asjc.312825:6(4232-4243)Online publication date: 16-Nov-2023
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Chen LLü S(2022)A fully discrete spectral scheme for time fractional Cahn-Hilliard equation with initial singularityComputers & Mathematics with Applications10.1016/j.camwa.2022.10.015127:C(213-224)Online publication date: 1-Dec-2022
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Wang YZheng Z(2022)A second-order L2-1 Crank-Nicolson difference method for two-dimensional time-fractional wave equations with variable coefficientsComputers & Mathematics with Applications10.1016/j.camwa.2022.05.018118:C(183-207)Online publication date: 15-Jul-2022
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Zhang GHuang CFei MWang N(2021)A linearized high-order Galerkin finite element approach for two-dimensional nonlinear time fractional Klein-Gordon equationsNumerical Algorithms10.1007/s11075-020-00978-787:2(551-574)Online publication date: 1-Jun-2021
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