Crank–Nicholson difference method and reproducing kernel function for third order fractional differential equations in the sense of Atangana–Baleanu Caputo derivative
By Ali Akgül, Mahmut Modanlı. Chaos, Solitons & Fractals, 2019
62 citations recorded by the source corpus.
Abstract In this paper, the third order partial differential equation defined by Caputo fractional derivative with Atangana–Baleanu derivative has been investigated. The stability estimates are proved for the exact solution. Difference schemes for Crank–Nicholson finite difference scheme method is constructed. The stability of difference schemes for this problem is shown by Von Neumann method (Fourier analysis method). Numerical results with respect to the exact solution confirm the accuracy and effectiveness of the technique. The reproducing kernel function for the problem has been found.
Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/4fdc022191c347d29c4519100f529c070c9eac7e
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In Applied Mathematics
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Citations in the corpus
- A study on fractional predator–prey–pathogen model with Mittag–Leffler kernel‐based operators (2020, methodology): “For example, some of these meth-ods are Reproducing kernel Hilbert space method [31, 32], Crank–Nicholson difference method [33], Variational approach [34, 35], q-homotopy analysis method [36], Laplace HPM [37, 36], Numerical schemes [38, 39], fixed point technique [40, 41], predictor–corrector,…”