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A Finite Difference Scheme for the Fractional Laplacian on Non-uniform Grids

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Abstract

In this study, we analyze the convergence of the finite difference method on non-uniform grids and provide examples to demonstrate its effectiveness in approximating fractional differential equations involving the fractional Laplacian. By utilizing non-uniform grids, it becomes possible to achieve higher accuracy and improved resolution in specific regions of interest. Overall, our findings indicate that finite difference approximation on non-uniform grids can serve as a dependable and efficient tool for approximating fractional Laplacians across a diverse array of applications.

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Funding

The author is supported by the Spanish MINECO through Juan de la Cierva fellow-ship FJC2021-046953-I.

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  1. Departamento de Matemáticas Fundamentales, UNED, Madrid, Spain

    A. M. Vargas

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  1. A. M. Vargas
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Correspondence to A. M. Vargas.

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Vargas, A.M. A Finite Difference Scheme for the Fractional Laplacian on Non-uniform Grids. Commun. Appl. Math. Comput. (2023). https://doi.org/10.1007/s42967-023-00323-4

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