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W. Auzinger, J. Burkotova, I. Rachunkova, V. Wenin:
"Shooting methods for state-dependent impulsive boundary value problems, with applications";
in: "ASC Report 2/2018", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2018, ISBN: 978-3-902627-11-7, 1 - 19.

For impulsive boundary value problems whose solutions encounter disconti-nuities (jumps) at a priori not known positions depending on the solution itself, numerical methods have not been considered so far. We extend the well-known shooting approach to this case, combining Newton iteration with the numerical solution of impulsive initial value problems. We discuss condi-tions necessary for the procedure to be well-de˝ned, and we present numerical results for several examples obtained with an experimental code realized in MATLAB.1

nonlinear boundary value problems, state-dependent impulses, shooting method

http://www.asc.tuwien.ac.at/preprint/2018/asc02x2018.pdf