ON SOME NUMERICAL INTEGRATION CURVES FOR PDE IN NEIGHBORHOOD OF "BUTTERFLY" CATASTROPHE POINT

Oleg Yu. Khachay     (Ural Federal University, Ekaterinburg, Russian Federation)
Pavel A. Nosov     (Ural Federal University, Ekaterinburg, Russian Federation)

Abstract


We consider a three-dimensional nonlinear wave equation with the source term smoothly changing over time and space due to a small parameter. The behavior of solutions of this PDE near the typical “butterfly” catastrophe point is studied. In the framework of matched asymptotic expansions method we derive a nonlinear ODE of the second order depending on three parameters to search for the special solution describing the rapid restructuring of the solution of the PDE in a small neighborhood of the catastrophe point, matching with expansion in a more outer layer. Numerical integration curves of the equation for the leading term of the inner asymptotic expansion are obtained.

Keywords


Matched asymptotic expansions, Numerical integration, Butterfly catastrophe, Nonlinear ODE

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DOI: http://dx.doi.org/10.15826/umj.2016.2.011

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