https://doi.org/10.1140/epjp/s13360-024-04976-9
Regular Article
A linear B-spline interpolation/Galerkin finite element method for the two-dimensional Riesz space distributed-order diffusion-wave equation with error analysis
1
Department of Applied Mathematics, Faculty of Mathematics, Statistics and Computer Science, University of Tabriz, Tabriz, Iran
2
Research Department of Computational Algorithms and Mathematical Models, University of Tabriz, Tabriz, Iran
3
Department of Mathematics, Mathematics Research Center, Near East University TRNC, Mersin 10, Turkey
4
Faculty of Engineering and Natural Sciences, Istanbul Okan University, Istanbul, Turkey
5
Institute for the Future of Knowledge, University of Johannesburg, PO Box 524, Auckland Park 2006, Johannesburg, South Africa
Received:
28
April
2023
Accepted:
31
January
2024
Published online:
16
April
2024
This paper focuses on the distributed-order time-fractional diffusion-wave equations with the Riesz space fractional derivatives. A combined method based on the midpoint quadrature rule, linear B-spline interpolation, and the Galerkin finite element method is proposed to obtain the approximate solution. Two steps are used to calculate the approximate solution to this type of equation. The first step approximates the temporal direction by combining a midpoint quadrature rule and linear B-spline interpolation. In the second step, a Galerkin finite element method in the space direction is applied to compute a full-discrete method. Furthermore, the error estimate has been displayed to demonstrate unconditional stability and convergence. Finally, two numerical examples are reported to show the simplicity and efficiency of the proposed method.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
