Publications

Sacramento, M., Almeida, C. and Moreira, M. (2020), IFOHAM - A Generalization of the Picard-Lindeloff Iteration Method, Differential and Difference Equations With Applications, Vol. 333, pp. 497-516

IFOHAM (Iterative First order HAM) is an iterative technique based on the first order equation of the Homotopy Analysis Method (HAM). It can be shown that IFOHAM generalizes Picard-Lindeloff's iteration algorithm and can be used to solve nonlinear differential equations. In this work IFOHAM will be implemented in a symbolic computer environment and we will analyze and test its applicability to find series solutions of second order nonlinear differential equations with periodic solutions. In particular, we will show that the IFOHAM method is able to identify the fundamental frequencies as well as the amplitudes of such periodic solutions. Knowledge of these parameters is of particular importance in design and mainte­ nance activities as it characterizes the oscillatory behavior of many real systems with nonlinear responses. The results of tests performed using the IFOHAM method will be compared with results available in the literature using the HAM as well as with results obtained using classical numerical technique s to solve differential equations.

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