https://doi.org/10.1140/epjs/s11734-023-00946-x
Regular Article
Application of efficient hybrid local meshless method for the numerical simulation of time-fractional PDEs arising in mathematical physics and finance
1
Department of Statistics, College of Science, University of Jeddah, Jeddah, Saudi Arabia
2
Department of Mathematics, College of Sciences and Arts at Alkamil, University of Jeddah, Jeddah, Saudi Arabia
3
Operational Research Center in Healthcare, Near East University, 99138, Nicosia, TRNC Mersin 10, Turkey
4
Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
5
Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186, Rome, Italy
c hijaz.ahmad@neu.edu.tr, ahmad.hijaz@uninettuno.it
Received:
8
March
2023
Accepted:
2
July
2023
Published online:
31
July
2023
The article describes the implementation of an efficient hybrid local meshless technique for the numerical solution of a multi-term time-fractional mobile-immobile diffusion equation in the sense of Caputo derivative, which models an anomalous mobile-immobile solute transport process. The proposed meshless technique, based on the inverse multiquadric-cubic radial basis function, is used to discretize the space derivatives of the model, while for time derivatives, an implicit time integration is utilized. The recommended technique approximates the solution on a set of scattered/uniform nodes, leading to a sparse and well-conditioned coefficient matrix. The article focuses on the benefits of meshless techniques, emphasizing their meshless nature and ease of use in higher dimensions. The proposed technique’s numerical results are compared with analytical solutions for various test problems on both rectangular and non-rectangular computational domains. These comparisons demonstrate the successful applications and accuracy of the local meshless technique.
Copyright comment corrected publication 2023
Copyright comment 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.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2023. corrected publication 2023. 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.
