Abstract
Radial basis function-based finite difference (RBF-FD) schemes generalize finite difference methods, providing flexibility in node distribution as well as the shape of the domain. In this paper, we consider a numerical formulation based on RBF-FD for solving a time–space fractional diffusion problem defined using a fractional Laplacian operator. The model problem is simplified into a local problem in space using the Caffarelli–Silvestre extension method. The space derivatives in the resulting problem are then discretized using a local RBF-based finite difference method, while L1 approximation is used for the fractional time derivative. Results obtained using the proposed scheme are then compared with that given in the existing literature.
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Acknowledgements
The first author acknowledges CSIR, India, for the financial support through CSIR-JRF/SRF fellowship.
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The research of the corresponding author (Revathy) is supported by the Council of Scientific & Industrial Research (CSIR), India under Grant Number: 09/886(0001)/2019-EMR-I.
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JMR: Literature survey, implementation, manuscript preparation. GC: Ideation, supervision, manuscript editing.
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Revathy, J.M., Chandhini, G. Solution of space–time fractional diffusion equation involving fractional Laplacian with a local radial basis function approximation. Int. J. Dynam. Control 12, 237–245 (2024). https://doi.org/10.1007/s40435-023-01237-y
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DOI: https://doi.org/10.1007/s40435-023-01237-y