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The Finite Element Method for Stiff Ordinary Differential Equations
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DOI：10.3390/appliedmath6030040.png)
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Abstract
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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.
Keywords:
stiff ordinary differential equations (ODEs)
the finite element method
A-stable
order of superconvergence
exponential dichotomy
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A
IF:
0.7
Papers:
111
Citations:
0
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