Differential Equations and Computational Simulations III
Electron. J. Diff. Eqns., Conf. 01, 1997, pp. 81-95.

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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