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A note on the homotopy analysis method. (English) Zbl 1195.65104
Summary: The present work is devoted to using an analytic approach, namely the homotopy analysis method, to obtain convergent series solutions of strongly nonlinear problems. On the basis of the homotopy derivative concept described in [{\it J. Liao}, Sci. Sin. Ser. A 25, 983--992 (1982; Zbl 0496.90037)], a theorem is proved here which generalizes some lemmas and theorems provided in [Liao, loc. cit.; and {\it A. Molabahrami} and {\it F. Khani}, Nonlinear Anal., Real World Appl. 10, No. 2, 589--600 (2009; Zbl 1167.35483)]. Significant applicability of the theorem obtained here in some practical situations is demonstrated.

65L99Numerical methods for ODE
Full Text: DOI
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