Generalized Quasilinearization for Nonlinear Problems

1998. Auflage 1998
ISBN: 978-0-7923-5038-5
Verlag: Springer Us

Buch, Englisch, Band 440, 278 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 1310 g

Reihe: Mathematics and Its Applications

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).

Zielgruppe

Research

Autoren/Hrsg.

Lakshmikantham, V.

Vatsala, A S

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematik Allgemein

Inhaltsverzeichnis

1. First Order Differential Equations.- 2. First Order Differential Equations (Cont.).- 3. Second Order Differential Equations.- 4. Miscellaneous Extensions.- References.