Generalized Quasilinearization for Nonlinear Problems
(Sprache: Englisch)
The book provides a systematic development of generalized quasilinearization indicating the notions and technical difficulties that are encountered in the unified approach. It enhances considerably the usefulness of the method of quasilinearization which...
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The book provides a systematic development of generalized quasilinearization indicating the notions and technical difficulties that are encountered in the unified approach. It enhances considerably the usefulness of the method of quasilinearization which has proved to be very effective in several areas of investigation and in applications. Further it includes the well-known monotone iterative technique as a special case.
Audience: Researchers, industrial and engineering scientists.
Klappentext zu „Generalized Quasilinearization for Nonlinear Problems “
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).
Inhaltsverzeichnis zu „Generalized Quasilinearization for Nonlinear Problems “
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. FunctionalDifferential Equations. 4.4. Impulsive Differential Equations. 4.5. Stochastic Differential Equations. 4.6. Differential Equations in a Banach Space. 4.7. Notes. References. Index.
Bibliographische Angaben
- Autoren: A. S. Vatsala , V. Lakshmikantham
- 1998, 278 Seiten, Maße: 23,4 x 15,6 cm, Gebunden, Englisch
- Verlag: Springer
- ISBN-10: 0792350383
- ISBN-13: 9780792350385
Sprache:
Englisch
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