Hikal, Manal M.Baleanu, DumitruZahra, Waheed K.2022-08-232025-09-182022-08-232025-09-182021Zahra, Waheed K.; Hikal, Manal M.; Baleanu, Dumitru (2021). "Numerical simulation for time-fractional nonlinear reaction-diffusion system on a uniform and nonuniform time stepping", MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Vol. 44, No. 7, pp. 5340-5364.0170-42141099-1476https://doi.org/10.1002/mma.7114https://hdl.handle.net/20.500.12416/14353Hikal, Manal/0000-0001-8339-0742; Zahra, Waheed K/0000-0002-6448-6877In 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.eninfo:eu-repo/semantics/closedAccessCaputo Fractional DerivativeConvergence AnalysisExponential FittingNonuniform Time SteppingStabilityArticle10.1002/mma.71142-s2.0-85101833378