Bibliographic Details
| Title: |
The Finite Element Method for Stiff Ordinary Differential Equations. |
| Authors: |
Ding, Yanhui, Tang, Qiong, Tang, Sijia |
| Source: |
AppliedMath; Mar2026, Vol. 6 Issue 3, p40, 20p |
| Subject Terms: |
Finite element method, Ordinary differential equations, Exponential dichotomy, Stability (Mechanics), Autonomous differential equations, Numerical analysis |
| Abstract: |
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. [ABSTRACT FROM AUTHOR] |
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| Database: |
Complementary Index |