A barycentric rational collocation method for higher-order equations related to time

Abstract In this article, higher-order equations related to time are solved using the barycentric rational collocation method, which aims to approximate the unknown function through a rational function. The equations are solved by using the direct solution, depression of order, and spatial using the barycentric rational collocation method, and then solved by the Runge-Kutta method in three ways. The final example verifies the validity.