2021
DOI: 10.1007/s11075-021-01121-w
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Numerical blow-up analysis of the explicit L1-scheme for fractional ordinary differential equations

Abstract: This paper deals with the blow-up behavior of numerical solutions to nonlinear fractional ordinary differential equations with a dissipative term. Based on the positivity preservation of the explicit L1-scheme, it is shown that for sufficiently small initial values, numerical solutions exist globally. Whereas for large initial values, numerical solutions with a suitable adaptive step strategy blow up in finite time. Finally, some numerical experiments are provided for verifying the theoretical analysis.

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