Numerical Blow-up Diagnostics for Differential equation solutionsстатья

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[1] Belov A. A., Korpusov M. O. Numerical blow-up diagnostics for differential equation solutions // Progress In Electromagnetics Research Symposium - Spring (PIERS), St Petersburg, Russia, 22-25 May. — IEEE Xplore Digital Library. — IEEE, 2017. — P. 2637–2643. In many actual non-linear differential equations, solutions may undergo blow-up regimes. In the present paper, we propose a new numerical technique of blow-up diagnostics for ordinary differential equations (ODEs). It allows to determine the singularity type (power pole, logarithmic pole or their multiplication) for the solution and its derivatives with confidence. The blow-up moment and the singularity type are calculated simultaneously with their a posteriori asymptotically precise error value. This method is applicable in arc length argument which is optimal for such problems. It is generalized to partial differential equations (PDEs) since in numerical solving they are reduced to a large system of ODEs. The proposed method is illustrated on a set of imposing examples. It is realized as an applied program package SiDiaG. The latter is distributed under free licence and can be downloaded at https://bitbucket.org/alexander belov/sidiag. Such software was not proposed earlier. [ DOI ]

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