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Numerical Solution of Nonstationary Problems for a Space-Fractional Diffusion Equation

  • Petr N. Vabishchevich EMAIL logo
Veröffentlicht/Copyright: 9. März 2016
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Fractional Calculus and Applied Analysis
Aus der Zeitschrift Fractional Calculus and Applied Analysis Band 19 Heft 1

Abstract

An unsteady problem is considered for a space-fractional diffusion equation in abounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary conditions of Robin type. Finite element approximation in space is employed. To construct approximation in time, regularized two-level schemes are used. The numerical implementation is based on solving the equation with the fractional power of the elliptic operator using an auxiliary Cauchy problem for a pseudo-parabolic equation. The results of numerical experiments are presented for a model two-dimensional problem.

MSC: Primary 26A33; Secondary 35R11; 65F60; 65M06
Key Words and Phrases: fractional partial differential equations; elliptic operator; fractional power of an operator; two-level difference scheme

Acknowledgements

This work was supported by the Russian Foundation for Basic Research (Projects 14-01-00785, 15-01-00026).

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  1. Please cite to this paper as published in:

    Fract. Calc. Appl. Anal., Vol. 19, No 1 (2016), pp. 116–139, DOI: 10.1515/fca-2016-0007

Received: 2014-12-5
Revised: 2015-7-9
Published Online: 2016-3-9
Published in Print: 2016-2-1

© 2016 Diogenes Co., Sofia

Artikel in diesem Heft

  1. Frontmatter
  2. Editorial
  3. FCAA Related News, Events and Books (FCAA–Volume 19–1–2016)
  4. Research Paper
  5. Smallest Eigenvalues for a Right Focal Boundary Value Problem
  6. Research Paper
  7. High-Order Algorithms for Riesz Derivative and their Applications (III)
  8. Research Paper
  9. Existence and Uniqueness for a Class of Stochastic Time Fractional Space Pseudo-Differential Equations
  10. Research Paper
  11. Error estimates for approximations of distributed order time fractional diffusion with nonsmooth data
  12. Research Paper
  13. Bogolyubov-Type Theorem with Constraints Generated by a Fractional Control System
  14. Research Paper
  15. Numerical Solution of Nonstationary Problems for a Space-Fractional Diffusion Equation
  16. Research Paper
  17. Solving 3D Time-Fractional Diffusion Equations by High-Performance Parallel Computing
  18. Discussion Survey
  19. Physical and Geometrical Interpretation of Grünwald-Letnikov Differintegrals: Measurement of Path and Acceleration
  20. Discussion Survey
  21. Some Applications of Fractional Velocities
  22. Research Paper
  23. Maximum Principles for Multi-Term Space-Time Variable-Order Fractional Diffusion Equations and their Applications
  24. Survey Paper
  25. Atypical Case of the Dielectric Relaxation Responses and its Fractional Kinetic Equation
  26. Research Paper
  27. Operator Method for Construction of Solutions of Linear Fractional Differential Equations with Constant Coefficients
  28. Research Article
  29. On the Existence and Multiplicity of Solutions for Dirichlet’s problem for Fractional Differential equations
  30. Research Paper
  31. Approximate controllability for semilinear composite fractional relaxation equations
https://doi.org/10.1515/fca-2016-0007
Schlagwörter für diesen Artikel
fractional partial differential equations; elliptic operator; fractional power of an operator; two-level difference scheme

Artikel in diesem Heft

  1. Frontmatter
  2. Editorial
  3. FCAA Related News, Events and Books (FCAA–Volume 19–1–2016)
  4. Research Paper
  5. Smallest Eigenvalues for a Right Focal Boundary Value Problem
  6. Research Paper
  7. High-Order Algorithms for Riesz Derivative and their Applications (III)
  8. Research Paper
  9. Existence and Uniqueness for a Class of Stochastic Time Fractional Space Pseudo-Differential Equations
  10. Research Paper
  11. Error estimates for approximations of distributed order time fractional diffusion with nonsmooth data
  12. Research Paper
  13. Bogolyubov-Type Theorem with Constraints Generated by a Fractional Control System
  14. Research Paper
  15. Numerical Solution of Nonstationary Problems for a Space-Fractional Diffusion Equation
  16. Research Paper
  17. Solving 3D Time-Fractional Diffusion Equations by High-Performance Parallel Computing
  18. Discussion Survey
  19. Physical and Geometrical Interpretation of Grünwald-Letnikov Differintegrals: Measurement of Path and Acceleration
  20. Discussion Survey
  21. Some Applications of Fractional Velocities
  22. Research Paper
  23. Maximum Principles for Multi-Term Space-Time Variable-Order Fractional Diffusion Equations and their Applications
  24. Survey Paper
  25. Atypical Case of the Dielectric Relaxation Responses and its Fractional Kinetic Equation
  26. Research Paper
  27. Operator Method for Construction of Solutions of Linear Fractional Differential Equations with Constant Coefficients
  28. Research Article
  29. On the Existence and Multiplicity of Solutions for Dirichlet’s problem for Fractional Differential equations
  30. Research Paper
  31. Approximate controllability for semilinear composite fractional relaxation equations
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