Abstract
A fixed mesh variational formulation is used to establish existence and uniqueness of the solution of ordinary differential equations with (infinitely many) state-dependent impulses on the right-hand side. This approach gives a natural numerical scheme to approximate the solution. The convergence of the approximation is proved and its asymptotic order obtained.
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This work has been supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC grant) and by the “Ministère del' Education du Québec” (FCAR grant).
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Dubeau, F. Existence, uniqueness and approximation of the solution of an ode with (infinitely many) state-dependent impulses via fixed mesh galerkin formulation. Approx. Theory & its Appl. 15, 55–73 (1999). https://doi.org/10.1007/BF02836792
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DOI: https://doi.org/10.1007/BF02836792