A Difference Method for Solving the Steklov Nonlocal Boundary Value Problem of Second Kind for the Time-Fractional Diffusion Equation

@article{Alikhanov2017ADM,
  title={A Difference Method for Solving the Steklov Nonlocal Boundary Value Problem of Second Kind for the Time-Fractional Diffusion Equation},
  author={Anatoly A. Alikhanov},
  journal={Computational Methods in Applied Mathematics},
  year={2017},
  volume={17},
  pages={1 - 16}
}
  • A. Alikhanov
  • Published 30 April 2014
  • Mathematics
  • Computational Methods in Applied Mathematics
Abstract We consider difference schemes for the time-fractional diffusion equation with variable coefficients and nonlocal boundary conditions containing real parameters α, β and γ. By the method of energy inequalities, for the solution of the difference problem, we obtain a priori estimates, which imply the stability and convergence of these difference schemes. The obtained results are supported by the numerical calculations carried out for some test problems. 

A second order difference scheme for time fractional diffusion equation with generalized memory kernel

Stability and convergence of the given schemes in the grid L2 norm with the rate equal to the order of the approximation error are proved.

A Time-Fractional Diffusion Equation with Generalized Memory Kernel in Differential and Difference Settings with Smooth Solutions

An a priori estimate for the corresponding differential problem is obtained by using the method of the energy inequalities using a difference analog of the Caputo fractional derivative with generalized memory kernel (L1 formula).

Устойчивость и сходимость разностных схем для уравнения диффузии дискретно-распределенного порядка с обобщенными функциями памяти

In this paper, a priori estimate for the corresponding differential problem is obtained by using the method of the energy inequalities. We construct a difference analog of the multi-term Caputo

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