Numerical detection and study of singularities in solutions of differential equations
- Authors: Belov A.A.1,2
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Affiliations:
- Keldysh Institute of Applied Mathematics
- Faculty of Physics
- Issue: Vol 93, No 3 (2016)
- Pages: 334-338
- Section: Computer Science
- URL: https://journals.rcsi.science/1064-5624/article/view/223926
- DOI: https://doi.org/10.1134/S1064562416020010
- ID: 223926
Cite item
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 characteristics 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 systems of ordinary differential equations of huge orders. The simplicity and reliability of the approach are superior to those of previously known methods.
About the authors
A. A. Belov
Keldysh Institute of Applied Mathematics; Faculty of Physics
Author for correspondence.
Email: belov_25.04.1991@mail.ru
Russian Federation, Miusskaya pl. 4, Moscow, 125047; Moscow, 119992