Generalized Quasilinearization for Nonlinear Problems

di V. Lakshmikantham (Autore)

A.S. Vatsala (Autore)

Springer, 1998

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).

• Autore: V. Lakshmikantham, A.S. Vatsala
• Editore: Springer
• Collana: Mathematics and Its Applications
• Anno: 1998
• Rilegatura: Hardback
• Pagine: 278 p.
• Dimensioni: 235 x 155 mm
• EAN: 9780792350385

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