# 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} }

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.

## 6 Citations

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

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- 2021

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

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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).

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### Finite difference/generalized Hermite spectral method for the distributed-order time-fractional reaction-diffusion equation on multi-dimensional unbounded domains

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- Mathematics
- 2019

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…

### Stable Numerical Schemes For Time-Fractional Diffusion Equation With Generalized Memory Kernel

- MathematicsApplied Numerical Mathematics
- 2021

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