Abstract
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.
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Original Russian Text © A.A. Belov, 2017, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2017, Vol. 57, No. 1, pp. 111–121.
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Belov, A.A. Numerical diagnostics of solution blowup in differential equations. Comput. Math. and Math. Phys. 57, 122–132 (2017). https://doi.org/10.1134/S0965542517010031
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DOI: https://doi.org/10.1134/S0965542517010031