Abstract.
Recently, Atangana and Batogna suggested a new numerical scheme to solve linear and non-linear equations with classical and fractional differential operators. The method can be understood as a combination of forward (or backward) approximation and the Adams-Bashforth one. This paper further presents the application of the new method to a linear and non-linear partial differential equation with integer- and non-integer-order derivative. The stability and convergence analyses are presented in detail. Some simulations are done to verify the efficiency of the new numerical scheme for solving linear and non-linear equations.
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Alkahtani, B.S.T. Atangana-Batogna numerical scheme applied on a linear and non-linear fractional differential equation. Eur. Phys. J. Plus 133, 111 (2018). https://doi.org/10.1140/epjp/i2018-11961-8
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DOI: https://doi.org/10.1140/epjp/i2018-11961-8