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- W3172025924 abstract "<abstract> A nonlinear initial value problem whose differential operator is a Caputo derivative of order $ alpha $ with $ 0 < alpha < 1 $ is studied. By using the Riemann-Liouville fractional integral transformation, this problem is reformulated as a Volterra integral equation, which is discretized by using the right rectangle formula. Both a priori and an a posteriori error analysis are conducted. Based on the a priori error bound and mesh equidistribution principle, we show that there exists a nonuniform grid that gives first-order convergent result, which is robust with respect to $ alpha $. Then an a posteriori error estimation is derived and used to design an adaptive grid generation algorithm. Numerical results complement the theoretical findings. </abstract>" @default.
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- W3172025924 date "2021-01-01" @default.
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- W3172025924 title "Analysis of a finite difference scheme for a nonlinear Caputo fractional differential equation on an adaptive grid" @default.
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- W3172025924 doi "https://doi.org/10.3934/math.2021500" @default.
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