Generalized Quasilinearization for Nonlinear Problems (Mathematics and Its Applications, 440)

Lakshmikantham, V.; Vatsala, A.S.

ISBN 10: 0792350383 / ISBN 13: 9780792350385

Published by Springer, 1998

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Bibliographic Details

• Title: Generalized Quasilinearization for Nonlinear Problems (Mathematics and Its Applications, 440)
• Publisher: Springer
• Publication Date: 1998
• Language: English
• ISBN 10: 0792350383
• ISBN 13: 9780792350385
• Binding: Hardcover
• Condition: New

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Synopsis

The problems of modern society are complex, interdisciplinary and nonlin- ear. onlinear problems are therefore abundant in several diverse disciplines. Since explicit analytic solutions of nonlinear problems in terms of familiar, well- trained functions of analysis are rarely possible, one needs to exploit various approximate methods. There do exist a number of powerful procedures for ob- taining approximate solutions of nonlinear problems such as, Newton-Raphson method, Galerkins method, expansion methods, dynamic programming, itera- tive techniques, truncation methods, method of upper and lower bounds and Chapligin method, to name a few. Let us turn to the fruitful idea of Chapligin, see [27] (vol I), for obtaining approximate solutions of a nonlinear differential equation u' = f(t, u), u(O) = uo. Let fl' h be such that the solutions of 1t' = h (t, u), u(O) = uo, and u' = h(t, u), u(O) = uo are comparatively simple to solve, such as linear equations, and lower order equations. Suppose that we have h(t, u) s f(t, u) s h(t, u), for all (t, u).