Abstract
An efficient and easily applicable, approximate analytic technique for the solution of nonlinear initial and boundary-value problems associated with nonlinear ordinary differential equations (O.D.E.) of any order and variable coefficients, is presented. Convergence, uniqueness and upper bound error estimates of solutions, obtained by the successive approximations scheme of the proposed technique, are thoroughly established. Important conclusions regarding the improvement of convergence for large time and large displacement solutions in case of nonlinear initial-value problems are also assessed. The proposed technique is much more efficient than the perturbations schemes for establishing the large postbuckling response of structural systems. The efficiency, simplicity and reliability of the proposed technique is demonstrated by two illustrative examples for which available numerical results exist.
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Communicated by D. E. Beskos, August 14, 1991
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Kounadis, A.N. An efficient and simple approximate technique for solving nonlinear initial and boundary-value problems. Computational Mechanics 9, 221–231 (1992). https://doi.org/10.1007/BF00350188
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DOI: https://doi.org/10.1007/BF00350188