{ "item_title" : "Generalized Quasilinearization for Nonlinear Problems", "item_author" : [" V. Lakshmikantham", "A. S. Vatsala "], "item_description" : "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, see27] (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).", "item_img_path" : "https://covers2.booksamillion.com/covers/bam/0/79/235/038/0792350383_b.jpg", "price_data" : { "retail_price" : "169.99", "online_price" : "169.99", "our_price" : "169.99", "club_price" : "169.99", "savings_pct" : "0", "savings_amt" : "0.00", "club_savings_pct" : "0", "club_savings_amt" : "0.00", "discount_pct" : "10", "store_price" : "" } }

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