Ahmad, Bashir; Alsaedi, Ahmed; Alghamdi, Badra S. Analytic approximation of solutions of the forced Duffing equation with integral boundary conditions. (English) Zbl 1154.34311 Nonlinear Anal., Real World Appl. 9, No. 4, 1727-1740 (2008). Summary: A sequence of approximate solutions converging monotonically and quadratically to the unique solution of the forced Duffing equation with integral boundary conditions is obtained. We also establish the convergence of order \(k(k\geqslant 2)\) for the sequence of iterates. The results obtained in this paper offer an algorithm to study the various practical phenomena such as prediction of the possible onset of vascular diseases, onset of chaos in speech, etc. Some interesting observations are presented. Cited in 88 Documents MSC: 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations Keywords:Duffing equation; integral boundary conditions; quasilinearization; quadratic convergence; higher order convergence PDFBibTeX XMLCite \textit{B. Ahmad} et al., Nonlinear Anal., Real World Appl. 9, No. 4, 1727--1740 (2008; Zbl 1154.34311) Full Text: DOI References: [1] Abd-Ellateef Kamar, A. R.; Drici, Z., Generalized quasilinearization method for systems of nonlinear differential equations with periodic boundary conditions, Dynam. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 12, 77-85 (2005) · Zbl 1092.34508 [2] Ahmad, B., A quasilinearization method for a class of integro-differential equations with mixed nonlinearities, Nonlinear Anal. Real World Appl., 7, 997-1004 (2006) · Zbl 1111.45005 [3] B. Ahmad, B. 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