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• W4313362370 abstract "A weak singularity in the solution of time-fractional differential equations can degrade the accuracy of numerical methods when employing a uniform mesh, especially with schemes involving the Caputo derivative (order α,), where time accuracy is of the order (2−α) or (1+α). To deal with this problem, we present a second-order numerical scheme for nonlinear time–space fractional reaction–diffusion equations. For spatial resolution, we employ a matrix transfer technique. Using graded meshes in time, we improve the convergence rate of the algorithm. Furthermore, some sharp error estimates that give an optimal second-order rate of convergence are presented and proven. We discuss the stability properties of the numerical scheme and elaborate on several empirical examples that corroborate our theoretical observations." @default.
• W4313362370 created "2023-01-06" @default.
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• W4313362370 date "2022-12-30" @default.
• W4313362370 modified "2023-09-27" @default.
• W4313362370 title "A Second-Order Crank-Nicolson-Type Scheme for Nonlinear Space–Time Reaction–Diffusion Equations on Time-Graded Meshes" @default.
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• W4313362370 doi "https://doi.org/10.3390/fractalfract7010040" @default.
• W4313362370 hasPublicationYear "2022" @default.
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