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A numerical algorithm for blow-up problems revisited

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Abstract

In many evolution equations, solutions may become unbounded in finite time. This phenomenon is often called blow-up and the finite time is called the blow-up time. To numerically reproduce the finite-time blow-up phenomenon, schemes with adaptive time meshes were considered to be necessary. Since the numerical blow-up time is defined by an infinite sum, which implies that one needs to compute infinite times to achieve blow-up, this method cannot be carried out in real computation. As a consequence, Cho (Jpn. J. Indust. Appl. Math. 30, 331–349 2013) proposed an algorithm accomplished by schemes with uniform time meshes for the computation of blow-up solutions. In this paper, we are concerned with a question: to what extent can this algorithm be applied to compute the blow-up solutions and reproduce the blow-up behavior?

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  1. Department of Mathematics, National Chung Cheng University, 168 University Road, Min-Hsiung Township, Chiayi County, 62102, Taiwan

    C.-H. Cho

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Cho, CH. A numerical algorithm for blow-up problems revisited. Numer Algor 75, 675–697 (2017). https://doi.org/10.1007/s11075-016-0216-6

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