Generalized Quasilinearization for Nonlinear Problems
Seiten
2010
|
Softcover reprint of hardcover 1st ed. 1998
Springer-Verlag New York Inc.
978-1-4419-4794-9 (ISBN)
Springer-Verlag New York Inc.
978-1-4419-4794-9 (ISBN)
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).
1. First Order Differential Equations.- 2. First Order Differential Equations (Cont.).- 3. Second Order Differential Equations.- 4. Miscellaneous Extensions.- References.
Erscheint lt. Verlag | 6.12.2010 |
---|---|
Reihe/Serie | Mathematics and Its Applications ; 440 |
Zusatzinfo | X, 278 p. |
Verlagsort | New York, NY |
Sprache | englisch |
Maße | 160 x 240 mm |
Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
Mathematik / Informatik ► Mathematik ► Analysis | |
ISBN-10 | 1-4419-4794-9 / 1441947949 |
ISBN-13 | 978-1-4419-4794-9 / 9781441947949 |
Zustand | Neuware |
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