Numerical Diagnostics of Solution Blowup in Differential Equationsстатья
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Дата последнего поиска статьи во внешних источниках: 1 апреля 2017 г.
Аннотация:New simple and robust methods have been proposed for detecting poles, logarithmic poles,
and mixed-type singularities in systems of ordinary differential equations. The methods produce characteristics of these singularities with a posteriori asymptotically precise error estimates. This approach is applicable to an arbitrary parametrization of integral curves, including the arc length parametrization, which is optimal for stiff and ill-conditioned problems. The method can be used to detect solution blowup for a broad class of important nonlinear partial differential equations, since they can be reduced to huge-order systems of ordinary differential equations by applying the method of lines. The method is superior in robustness and simplicity to previously known methods.