## Colloquium: “Filtered LeapFrog Time Integration with Enhanced Stability Properties”

Marshall University Math Colloquium

October 30, 2013

Roger Estep

*Marshall University*

**Abstract**

The Leapfrog method for the solution of Ordinary Differential Equation initial value has been historically popular for several reasons. The method has second order accuracy, requires only one function evaluation per time step, and is non-dissipative. Despite the mentioned attractive properties, the method has some unfavorable stability properties. The absolute stability region of the method is only an interval located on the imaginary axis rather than a region in the complex plane. The method is only weakly stable and thus exhibits computational instability in long time integrations over intervals of finite length. In this work the use of filters is examined for the purposes of both controlling the weak instability and also enlarging the size of the absolute stability region of the method.