Variable step size destabilizes the Störmer/leapfrog/verlet method
Copyright policy )Variable step size destabilizes the Störmer/leapfrog/verlet method
The effect of variable step sizes is studied for the second order Störmer method applied to the standard test equation \(y'' = -\omega^ 2y\). It is shown that instabilities may occur, even in the case where \(\omega h_ n\) is small and the step size ratio \(h_ n/h_{n-1}\) is limited.
- University of Illinois at Urbana Champaign United States
Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, second order Störmer method, Verlet method, variable step sizes, test equation, instabilities, Linear ordinary differential equations and systems, Mesh generation, refinement, and adaptive methods for ordinary differential equations, leapfrog method, Stability and convergence of numerical methods for ordinary differential equations
Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, second order Störmer method, Verlet method, variable step sizes, test equation, instabilities, Linear ordinary differential equations and systems, Mesh generation, refinement, and adaptive methods for ordinary differential equations, leapfrog method, Stability and convergence of numerical methods for ordinary differential equations
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