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Armenian Journal of Mathematics=Հայկական մաթեմատիկական հանդես
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Title:
Numerical Blow-Up Analysis of Explicit L1 Scheme for Time-Fractional Partial Differential Equations
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Գլխ. խմբ.՝ Անրի Ներսեսյան ; Պատ. խմբ.՝ Լինդա Խաչատրյան ; Խմբ. տեղակալ՝ Ռաֆայել Բարխուդարյան
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Time-Fractional Partial Differential Equations ; Explicit L1 Scheme ; Blow-Up
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Abstract:
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 intro- duce 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 fnite blow-up behaviors of numerical solution are studied. Finally, some numerical examples for verifying the theoretical results are provided.
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Electronic Open Access Publication of the National Academy of Sciences of Armenia