Stability and convergence of an implicit numerical method for the space and time fractional Bloch–Torrey equation

DOI10.1098/rsta.2012.0150zbMath1339.65151OpenAlexW2161458168WikidataQ34644685 ScholiaQ34644685MaRDI QIDQ2809800

Ian W. Turner, Kevin Burrage, Fawang Liu, Qiang Yu

Publication date: 30 May 2016

Published in: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1098/rsta.2012.0150

zbMATH Keywords

stabilityconvergencenumerical resultserror analysisfinite differenceimplicit numerical methodBloch-Torrey equationspace and time fractional Bloch-Torrey equation

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

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Cites Work

• Fractional Bloch equation with delay
• Numerical approximations and solution techniques for the space-time Riesz-Caputo fractional advection-diffusion equation
• Numerical solutions for fractional reaction-diffusion equations
• Numerical methods for fractional partial differential equations with Riesz space fractional derivatives
• Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation
• Numerical solution of the space fractional Fokker-Planck equation.
• Chaos, fractional kinetics, and anomalous transport
• Finite difference approximations for fractional advection-dispersion flow equations