Numerical analysis of strongly nonlinear oscillation systems using He’s max-min method

Abstract

Nonlinear functions are crucial points and terms in engineering problems. Actual and physical problems can be solved by solving and processing such functions. Thus, most scientists and engineers focus on solving these equations. This paper presents a novel method called the max-min method for presenting an accurate approximate analytical solution to strong nonlinear oscillators. It can solve many linear or nonlinear differential equations without the tangible restriction of sensitivity to the degree of the nonlinear term. It is also quite convenient due to the reduction in the size of calculations. The algorithm suggests a promising approach and is systematically illustrated step by step.

Keywords

min-max method / nonlinear oscillation / duffing equation / mathematical pendulum / He’s energy balance method

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