Penggunaan Metode Homotopi untuk Menyelesaikan Masalah Getaran Taklinear

Abstract

Nonlinear problem is a problem that contains nonlinear mathematical equation. One example of nonlinear problem is oscillation. Nonlinear problem is difficult to solve directly, so it needs an analytical approach. Homotopy method is one of the known analytical approaches. In this paper, nonlinear oscillation problem is solved using the homotopy method. The use of homotopy method is done by defining a homotopy function that requires auxiliary parameters to control the convergence region of the solution. The solutionis a recursive formula with given initial conditions. A case study using MAPLE shows that oscillation frequency and the equilibrium position converge to some certain values. This convergence of solution depends on the selection of auxiliary parameters in the homotopy function.