Vol. 18 No. 4 (2026): Numerical Blow-up Analysis for Fractional Ordinary Differential Equations with Linearly Implicit L1 Method

Published: 2026-04-30

Articles

  • Articles

    Numerical Blow-up Analysis for Fractional Ordinary Differential Equations with Linearly Implicit L1 Method

    Qi Wang, Zunkai Wang
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    Abstract

    In this paper, we consider the blow-up behavior of linearly implicit L1 method for fractional ordinary differential equations. Based on Nakagawa's criteria, a suitable adaptive step strategy is introduced. The existence of global numerical solution is proved. Moreover, we show that the finite blow-up behaviors are replicated for any positive solution. Finally, some numerical examples are given to test the main result.

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