Bigi, D.; Riganti, R. Solutions of nonlinear boundary value problems by the decomposition method. (English) Zbl 0592.60048 Appl. Math. Modelling 10, 49-52 (1986). Summary: Boundary value problems for a class of nonlinear operator equations are studied and a method for determining their solutions in approximated form is proposed, based on the Adomian decomposition procedure. The theory is applied with satisfactory results to the study of a classical boundary value problem in continuum mechanics. Cited in 10 Documents MSC: 60H99 Stochastic analysis 74A99 Generalities, axiomatics, foundations of continuum mechanics of solids Keywords:decomposition procedure; boundary value problem in continuum mechanics PDF BibTeX XML Cite \textit{D. Bigi} and \textit{R. Riganti}, Appl. Math. Modelling 10, 49--52 (1986; Zbl 0592.60048) Full Text: DOI References: [1] Adomian, G, Stochastic systems, (1983), Academic Press New York · Zbl 0504.60066 [2] Adomian, G, Nonlinear stochastic operator equations, (1986), Academic Press New York · Zbl 0614.35013 [3] Bellomo, N. and Riganti, R. ‘Time evolution of the probability density and the entropy function for a class of nonlinear stochastic systems in mathematical physics’, Comput. Math. Appl., special issue, memorial volume for Richard Bellman, (in press) · Zbl 0604.93052 [4] Riganti, R, Periodic solutions of a class of semi-linear stochastic differential equations with random parameters, (), 533 [5] Adomian, G; Bigi, D; Riganti, R, On the solution of stochastic initial value problems in continuum mechanics, J. math. analysis appl., 110, 442, (1985) · Zbl 0582.60066 [6] Adomian, G, Stabilization of stochastic nonlinear economy, J. math. analysis appl., 88, 306, (1982) · Zbl 0483.90025 [7] Adomian, G; Bellman, R, Biological system interactions, () · Zbl 0534.92003 [8] Nayfeh, A.H, Perturbation methods, (1979), Wiley New York · Zbl 0375.35005 [9] Hay, G.E, The finite displacement of thin rods, Trans. am. math. soc., 62, (1942) · Zbl 0061.42206 [10] Cicala, P, Asymptotic theory of elastic beams and rods, Meccanica, 2, 85, (1981) · Zbl 0485.73040 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.