Journal
MATHEMATICAL PROBLEMS IN ENGINEERING
Volume 2022, Issue -, Pages -Publisher
HINDAWI LTD
DOI: 10.1155/2022/2517602
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This study presents a novel numerical method to solve PDEs with the fractional Caputo operator. The method utilizes the Newton interpolation numerical scheme and inverse Laplace transform to solve fractional Buckmaster and diffusion equations, demonstrating high stability and fast convergence.
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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