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Approximation of solutions of the nonlinear Duffing equation involving both integral and non-integral forcing terms with separated boundary conditions. (English) Zbl 1197.34023

Summary: We study a boundary value problem involving the nonlinear Duffing equation with both integral and non-integral forcing terms, and separated boundary conditions. We develop a generalized quasilinearization algorithm to obtain monotone sequences of lower and upper solutions converging uniformly and quadratically to the unique solution of the problem.

MSC:

34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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