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arXiv · 1703.10202

New numerical methods for blow-up problems

Andrei D. Polyanin·Inna K. Shingareva
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Abstract

Two new methods of numerical integration of Cauchy problems for ODEs with blow-up solutions are described. The first method is based on applying a differential transformation, where the first derivative (given in the original equation) is chosen as a new independent variable. The second method is based on introducing a new non-local variable that reduces ODE to a system of coupled ODEs. Both methods lead to problems whose solutions do not have blowing-up singular points, therefore the standard numerical methods can be applied. The efficiency of the proposed methods is illustrated with several test problems.

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Andrei D. Polyanin, Inna K. Shingareva. 2017-03-29. New numerical methods for blow-up problems. https://arxiv.org/abs/1703.10202

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