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Quasilinearization of a boundary value problem for impulsive differential equations. (English) Zbl 0991.34027

The authors show the existence of a sequence of approximate solutions converging quadratically to a solution to an ordinary differential equation of first order with a boundary condition and subjected to impulses at fixed points. They generalize the result of V. Lakshmikantham and J. J. Nieto in [Nonlinear Times Dig. 2, No. 1, 1–9 (1995; Zbl 0855.34013)] on the nonimpulsive periodic boundary value problem.

MSC:

34B37 Boundary value problems with impulses for ordinary differential equations
34A37 Ordinary differential equations with impulses
34A45 Theoretical approximation of solutions to ordinary differential equations
65L10 Numerical solution of boundary value problems involving ordinary differential equations

Citations:

Zbl 0855.34013
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References:

[1] Bainov, D.D.; Simeonov, P.S., Integral inequalities and applications, (1992), Kluwer Academic Publishers Dordrecht · Zbl 1136.26003
[2] Lakshmikantham, V.; Nieto, J.J., Generalized quasilinearization for nonlinear first order ordinary differential equation, Nonlinear times digest, 2, 1-10, (1995) · Zbl 0855.34013
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