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A Hybrid Interpolation Method for Fractional PDEs and Its Applications to Fractional Diffusion and Buckmaster Equations
Mathematical Problems in Engineering ; 2022, 2022.
Article in English | ProQuest Central | ID: covidwho-1923337
ABSTRACT
This study presents a novel numerical method to solve PDEs with the fractional Caputo operator. In this method, we apply the Newton interpolation numerical scheme in Laplace space, and then, the solution is returned to real space through the inverse Laplace transform. The Newton polynomial provides good results as compared to the Lagrangian polynomial, which is used to construct the Adams–Bashforth method. This procedure is used to solve fractional Buckmaster and diffusion equations. Finally, a few numerical simulations are presented, ensuring that this strategy is highly stable and quickly converges to an exact solution.
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Full text: Available Collection: Databases of international organizations Database: ProQuest Central Language: English Journal: Mathematical Problems in Engineering Year: 2022 Document Type: Article

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Full text: Available Collection: Databases of international organizations Database: ProQuest Central Language: English Journal: Mathematical Problems in Engineering Year: 2022 Document Type: Article