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Volume 18, Issue 2
A Finite-Difference Scheme for a Linear Multi-Term Fractional-in-Time Differential Equation with Concentrated Capacities

Aleksandra Delić, Sandra Živanović & Zorica Milovanović Jeknić

Int. J. Numer. Anal. Mod., 18 (2021), pp. 265-286.

Published online: 2021-03

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  • Abstract

In this paper, we consider a linear multi-term subdiffusion equation with coefficients which contain Dirac distributions. Also, we consider subdiffusion equations with dynamical boundary conditions. The existence of generalized solutions of these initial-boundary value problems is proved. An implicit finite difference scheme is proposed and its stability and convergence rate are investigated in both cases. The corresponding difference schemes are tested on numerical examples.

  • Keywords

Fractional derivative, fractional PDE, boundary value problem, interface problem, finite differences.

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-18-265, author = {Delić , AleksandraŽivanović , Sandra and Milovanović Jeknić , Zorica}, title = {A Finite-Difference Scheme for a Linear Multi-Term Fractional-in-Time Differential Equation with Concentrated Capacities}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2021}, volume = {18}, number = {2}, pages = {265--286}, abstract = {

In this paper, we consider a linear multi-term subdiffusion equation with coefficients which contain Dirac distributions. Also, we consider subdiffusion equations with dynamical boundary conditions. The existence of generalized solutions of these initial-boundary value problems is proved. An implicit finite difference scheme is proposed and its stability and convergence rate are investigated in both cases. The corresponding difference schemes are tested on numerical examples.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/18711.html} }
TY - JOUR T1 - A Finite-Difference Scheme for a Linear Multi-Term Fractional-in-Time Differential Equation with Concentrated Capacities AU - Delić , Aleksandra AU - Živanović , Sandra AU - Milovanović Jeknić , Zorica JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 265 EP - 286 PY - 2021 DA - 2021/03 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/18711.html KW - Fractional derivative, fractional PDE, boundary value problem, interface problem, finite differences. AB -

In this paper, we consider a linear multi-term subdiffusion equation with coefficients which contain Dirac distributions. Also, we consider subdiffusion equations with dynamical boundary conditions. The existence of generalized solutions of these initial-boundary value problems is proved. An implicit finite difference scheme is proposed and its stability and convergence rate are investigated in both cases. The corresponding difference schemes are tested on numerical examples.

Aleksandra Delić, Sandra Živanović & Zorica Milovanović​ Jeknić. (2021). A Finite-Difference Scheme for a Linear Multi-Term Fractional-in-Time Differential Equation with Concentrated Capacities. International Journal of Numerical Analysis and Modeling. 18 (2). 265-286. doi:
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