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Finite Difference Approximation of a Generalized Time-Fractional Telegraph Equation

  • Aleksandra Delić , Boško S. Jovanović EMAIL logo and Sandra Živanović
Published/Copyright: August 20, 2019

Abstract

We consider a class of a generalized time-fractional telegraph equations. The existence of a weak solution of the corresponding initial-boundary value problem has been proved. A finite difference scheme approximating the problem is proposed, and its stability is proved. An estimate for the rate of convergence, in special discrete energetic Sobolev’s norm, is obtained. The theoretical results are confirmed by numerical examples.


Dedicated to the centenary of the birth of academician Alexander Andreevich Samarskii


Award Identifier / Grant number: 174015

Funding statement: This work was supported by Ministry of Education, Science and Technological Development of Republic of Serbia through project No. 174015.

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Received: 2018-11-26
Revised: 2019-07-09
Accepted: 2019-07-11
Published Online: 2019-08-20
Published in Print: 2020-10-01

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. Modern Problems of Numerical Analysis. On the Centenary of the Birth of Alexander Andreevich Samarskii
  4. Special Issue Articles
  5. Finite Difference Approximation of a Generalized Time-Fractional Telegraph Equation
  6. Weighted Estimates for Boundary Value Problems with Fractional Derivatives
  7. Lagrangian Mixed Finite Element Methods for Nonlinear Thin Shell Problems
  8. Reliable Computer Simulation Methods for Electrostatic Biomolecular Models Based on the Poisson–Boltzmann Equation
  9. Adaptive Space-Time Finite Element Methods for Non-autonomous Parabolic Problems with Distributional Sources
  10. On Convergence of Difference Schemes for Dirichlet IBVP for Two-Dimensional Quasilinear Parabolic Equations with Mixed Derivatives and Generalized Solutions
  11. Difference Schemes on Uniform Grids for an Initial-Boundary Value Problem for a Singularly Perturbed Parabolic Convection-Diffusion Equation
  12. A Finite Element Splitting Method for a Convection-Diffusion Problem
  13. Incomplete Iterative Implicit Schemes
  14. Explicit Runge–Kutta Methods Combined with Advanced Versions of the Richardson Extrapolation
  15. Regular Research Articles
  16. A General Superapproximation Result
  17. A First-Order Explicit-Implicit Splitting Method for a Convection-Diffusion Problem
  18. A Factorization of Least-Squares Projection Schemes for Ill-Posed Problems
  19. A New Mixed Functional-probabilistic Approach for Finite Element Accuracy
  20. Error Analysis of a Finite Difference Method on Graded Meshes for a Multiterm Time-Fractional Initial-Boundary Value Problem
  21. A Finite Element Method for Elliptic Dirichlet Boundary Control Problems
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