Numerical Detection and Study of Singularities
in Solutions of Differential Equations

A. A. Belov

Presented by Academician of the RAS B.N. Chetverushkin October 8, 2015

Received October 8, 2015

Abstract—New simple and robust methods are proposed for detecting singularities, such as poles, logarithmic
poles, and mixed singularities, in systems of ordinary differential equations. The methods produce characteris-
tics of these singularities with an a posteriori asymptotically precise error estimate. They are applicable in the
case of an arbitrary parametrization of integral curves, including one in terms of the arc length, which is optimal
for stiff and ill-conditioned problems. Following this approach, blowup solutions can be detected for a broad
class of important nonlinear partial differential equations, since they are reducible by the method of lines to sys-
tems of ordinary differential equations of huge orders. The simplicity and reliability of the approach are supe-
rior to those of previously known methods.

DOI: 10.1134/S1064562416020010

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