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Browsing by Author "Zahra, Waheed K."

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    Numerical Simulation for Time-Fractional Nonlinear Reaction-Diffusion System on a Uniform and Nonuniform Time Stepping
    (Wiley, 2021) Hikal, Manal M.; Baleanu, Dumitru; Zahra, Waheed K.
    In this article, two nonstandard high-order schemes on a uniform and nonuniform time stepping combined with the multi-parameter exponential fitting technique (MPEF) have been developed to solve the time-fractional nonlinear reaction-diffusion system. The first method based on the MPEF combined with the 3-weighted shifted-Grunwald-Letnikov approximation with uniform time stepping, this scheme leads to a numerical solution that suffers from the singularity near t = 0. In order to frustrate this singularity, a nonstandard higher-order L1-approximation for a nonuniform time-stepping scheme is developed. The developed scheme's convergence and unconditionally stability analysis have been verified. Numerical results effectively validate the theoretical aspects.