The Finite Element Method for Stiff Ordinary Differential Equations

The paper utilizes the continuous finite element method to solve stiff ordinary differential equations and proves that the linear finite element method and the quadratic finite element method have A-stability in solving autonomous ordinary differential equations, and exponential dichotomy in solving non-autonomous ordinary differential equations. In the numerical experiments of nonlinear autonomous and non-autonomous strongly and moderately stiff ordinary differential equations, a relatively large step size of h=0.1 was adopted over a longer period of time, with the numerical solution accuracy reaching 10−4. The superconvergence order maintained the theoretical order. A new approach is provided for solving stiff ordinary differential equations.