Analisis Metode Homotopi dalam Menyelesaikan Persamaan Lorenz

Abstract

Abstract Lorenz equations is one of the result of mathematical modeling of the three dimensional phenomenon of convection (air) in the atmosphere. In recent years, the Lorenz equations has attracted the attention of scientists and engineering because of the phenomenon chaos was produced. The complexity of the chaos produced cause the Lorenz equations to be very difficult to solve. This study aims to solve the Lorenz equations by using homotopy analysis method and then comparing it with the approximation on the ode45 solver. Solution using a homotopy method is done by constructing  a zero-order deformation equation into a high-order deformation equation. In this method there is freedom in choosing a auxiliary linear operator, initial approximation, and convergent–control parameter  that can guarantee the convergence solution. The resulting approximation is a series. The results of the study obtained 10th order homotopy approximation from the Lorenz equations, which is when  it approach the ode45 approximation. Unfortunatelly the period of homotopy approximation is a very short.Keywords Lorenz equations, Chaos, Homotopy Method.