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Nonlocal Singularities on Families of Periodic Solutions to Ordinary Differential Equations

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Abstract

We consider degenerate solutions on families of periodic solutions to ordinary differential equations. Degeneracy is understood as an arbitrary property of a solution that isolates this solution from generic cases. This can be either a bifurcation on a family or some topological peculiarity of the family, which causes a failure of a numerical algorithm applicable to generic cases. We suggest a means to compute these singular solutions with application of variational equations of higher order and with the same accuracy as ordinary solutions. The method is based on a symbolic recursive differentiation of an ODE with respect to initial values and parameters.

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  1. Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 125047, Moscow, Russia

    V. P. Varin

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  1. V. P. Varin
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Varin, V.P. Nonlocal Singularities on Families of Periodic Solutions to Ordinary Differential Equations. Comput. Math. and Math. Phys. 60, 53–64 (2020). https://doi.org/10.1134/S0965542520010145

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