Differential Equations and Computational Simulations III

Electron. J. Diff. Eqns., Conf. 01, 1997, pp. 81-95.

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Quadratic convergence of approximate solutions of two-point
boundary value problems with impulse

Vidya Doddaballapur, Paul W. Eloe, & Yongzhi Zhang

**Abstract:**

The method of quasilinearization, coupled with the method of
upper and lower solutions, is applied to a boundary value problem for an
ordinary differential equation with impulse that has a unique solution.
The method generates sequences of approximate solutions which converge
monotonically and quadratically to the unique solution. In this work, we
allow nonlinear terms with respect to velocity; in particular, Nagumo
conditions are employed.
Published November 12, 1998.

Mathematics Subject Classifications: 34A37, 34B15.

Key words: Quasilinearization, boundary value problem with
impulse, quadratic convergence, Nagumo conditions.

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Vidya Doddaballapur

Department of Mathematics,
University of Dayton

Dayton, Ohio 45469-2316, USA
Paul W. Eloe

Department of Mathematics,
University of Dayton

Dayton, Ohio 45469-2316, USA

Email address: eloe@saber.udayton.edu

Yongzhi Zhang

Department of Mathematics,
University of Dayton

Dayton, Ohio 45469-2316, USA

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