Analysis reveals finite blow-up behaviors in numerical solutions of time-fractional partial differential equations, indicating adaptive strategies are necessary.
In this paper, we consider the blow-up of explicit L1 scheme for time-fractional partial differential equations. Firstly, we discretize the mentioned equation by the explicit L1 scheme and obtain the corresponding matrix form. Secondly, we introduce the concept of discrete energy. Based on Nakagawa's criteria, a suitable adaptive time-stepping strategy is given by the discrete energy. Thirdly, with the help of lower discrete energy, the finite blow-up behaviors of numerical solution are studied. Finally, some numerical examples for verifying the theoretical results are provided.
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Qi Wang (2025) studied this question.
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