Implicit difference approximation for the time fractional heat equation with the nonlocal condition

DOI10.1016/j.apnum.2011.08.007zbMath1266.65146OpenAlexW2087273363MaRDI QIDQ651090

İbrahim Karatay, Şerife R. Bayramoğlu, Ali Şahin

Publication date: 8 December 2011

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2011.08.007

zbMATH Keywords

stabilitynumerical examplesSchur complementimplicit finite difference schemematrix stabilityKailath theoremmatrix block inversionmodified Gaussian eliminationnonlocal fractional parabolic differential equationtime fractional heat equation

Mathematics Subject Classification ID

Heat equation (35K05) 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) Finite difference methods applied to problems in thermodynamics and heat transfer (80M20) Fractional partial differential equations (35R11)

Related Items (11)

Chaotic and spatiotemporal oscillations in fractional reaction-diffusion system ⋮ A new Grünwald-Letnikov derivative derived from a second-order scheme ⋮ A characteristic difference scheme for time-fractional heat equations based on the Crank-Nicholson difference schemes ⋮ Solving a linear fractional equation with nonlocal boundary conditions based on multiscale orthonormal bases method in the reproducing kernel space ⋮ Approximate solution of the multi-term time fractional diffusion and diffusion-wave equations ⋮ On solutions of fractional order telegraph partial differential equation by Crank-Nicholson finite difference method ⋮ Novel numerical approach for time fractional equations with nonlocal condition ⋮ Two numerical methods for fractional partial differential equation with nonlocal boundary value problem ⋮ A fast collocation algorithm for solving the time fractional heat equation ⋮ A new difference scheme for time fractional heat equations based on the Crank-Nicholson method ⋮ Higher-dimensional physical models with multimemory indices: analytic solution and convergence analysis

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