Generalized Quasilinearization for Nonlinear Problems: 440 - Rilegato

Lakshmikantham, V.; Vatsala, A. S.

Rilegato

ISBN 10: 0792350383 ISBN 13: 9780792350385

Casa editrice: Kluwer Academic Pub, 1998

Riassunto

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).

Su questo libro

Contenuti

Preface. 1: First Order Differential Equations. 1.0. Introduction. 1.1. Method of Upper and Lower Solutions. 1.2. Method of Quasilinearization. 1.3. Extensions. 1.4. Generalizations. 1.5. Refinements. 1.6. Notes. 2: First Order Differential Equations. (Cont.) 2.0. Introduction. 2.1. Periodic Boundary Value Problems. 2.2. Anti-Periodic Boundary Value Problems. 2.3. Interval Analysis and Quasilinearization. 2.4. Higher Order Convergence. 2.5. Another Refinement of Quasilinearization. 2.6. Extension to System of Differential Equations. 2.7. Notes. 3: Second Order Differential Equations. 3.0. Introduction. 3.1. Method of Upper and Lower Solutions. 3.2. Extension of Quasilinearization. 3.3. Generalized Quasilinearization. 3.4. General Second Order BVP. 3.5. General Second Order BVP (cont.). 3.6. Higher Order Convergence. 3.7. Notes. 4: Miscellaneous Extensions. 4.0. Introduction. 4.1. Dynamic Systems on Time Scales. 4.2. Integro-Differential Equations. 4.3. Functional Differential Equations. 4.4. Impulsive Differential Equations. 4.5. Stochastic Differential Equations. 4.6. Differential Equations in a Banach Space. 4.7. Notes. References. Index.

Product Description

Book by Lakshmikantham V Vatsala AS

Dettagli dell?edizione

• Editore: Kluwer Academic Pub
• Data di pubblicazione: 1998
• ISBN 10: 0792350383
• ISBN 13: 9780792350385
• Rilegatura: Copertina rigida
• Lingua: Inglese
• Numero di pagine: 276