Numerical analysis for the fractional diffusion and fractional Buckmaster equation by the two-step Laplace Adam-Bashforth method
Department of Mathematics, Faculty of Science & Technology, The ICFAI University, 302031, Jaipur, India
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Accepted: 19 December 2017
Published online: 19 January 2018
In this paper, we aim to use the alternative numerical scheme given by Gnitchogna and Atangana for solving partial differential equations with integer and non-integer differential operators. We applied this method to fractional diffusion model and fractional Buckmaster models with non-local fading memory. The method yields a powerful numerical algorithm for fractional order derivative to implement. Also we present in detail the stability analysis of the numerical method for solving the diffusion equation. This proof shows that this method is very stable and also converges very quickly to exact solution and finally some numerical simulation is presented.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2018