An improved homotopy analysis method with accelerated convergence for nonlinear problems

Abstract

In this paper we propose an accelerated convergence method, which is combined with the homotopy analysis method (HAM), to solve nonlinear problems. The HAM is applied to obtain approximate expressions. According to the numbers of terms in the approximations, some ratio-control parameters are introduced in the solution expressions. By solving simultaneous algebraic equations, all artificial parameters can be optimally identified, including the so-called convergence-control parameter ℏ. Twoexamples are given to illustrate the validity of the new method. Comparison with L-P perturbation method and Runge-Kutta method reveals that the improved HAM is better than the standard HAM and applies especially to the problems with complicated nonlinear terms.

Research on the Design Method of Cushioning Packaging for Products with Unbalanced Mass

“…Sun [11] developed a nonlinear differential equation of motion of the buffered packaging system based on the Lagrange general dynamics equation, and solved the nonlinear differential equation by means of equal method, Markov method, perturbation method and simulation method. Li et al [12] evaluated the strong nonlinearity of the buffered packaging dynamics model using MMA and HAM algorithms and validated their accuracy through experiments. For the study of the vibration-response characteristics of buffered packaging, Hao [13] refined the vibration response characteristics of buffered packaging, focusing on the buffered packaging characteristics of vulnerable parts such as cantilever beams.…”