# 帕德逼近及在求解非线性系统中的应用Padé Approximation and Its Application in Solving Nonlinear Systems

Abstract: Many problems in engineer science and natural science are often summed up in solving nonlinear systems. For many years, the rational function approximation has attracted more and more attention, which is one of the typical nonlinear approximation approaches. We mainly study one of the classical rational function approximations—Padé approximation in this paper. We take the orthogonal function system as the base function, and study some Padé approximation problems under the base function of orthogonal trigonometric function and orthogonal polynomial function respectively. Then the approximation effect is demonstrated by the concrete examples. Finally, we combine the Padé approximation with the homotopy analysis method to solve the nonlinear system, and verify its effectiveness by a three-degree-of-freedom system.

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