Symplectic variable step size integration for N-body problems

Symplectic Integration with Variable Stepsize

There is considerable evidence suggesting that for Hamiltonian systems of ordinary differential equations it is better to use numerical integrators that preserve the symplectic property of the ow of the system, at least for long-time integrations. We present what we believe is a practical way of doing symplectic integration with variable stepsize. Another idea, orthogonal to variable stepsize, ...

Variable time step integration

Symplectic methods for Hamiltonian systems are known to have favourable properties concerning long-time integrations (no secular terms in the error of the energy integral, linear error growth in the angle variables instead of quadratic growth, correct qualitative behaviour) if they are applied with constant step sizes, while all of these properties are lost in a standard variable step size impl...

Variable Step-size Selection Methods for Implicit Integration Schemes for Odes

Implicit integration schemes for ODEs, such as Runge-Kutta and Runge-Kutta-Nyström methods, are widely used in mathematics and engineering to numerically solve ordinary differential equations. Every integration method requires one to choose a step-size, h, for the integration. If h is too large or too small the efficiency of an implicit scheme is relatively low. As every implicit integration sc...

A new variable step size block backward differentiation formula for solving stiff initial value problems

A Variable Step-Size Exponentially Fitted Explicit Hybrid Method for Solving Oscillatory Problems

An exponentially fitted explicit hybrid method for solving oscillatory problems is obtained. This method has four stages. The first three stages of the method integrate exactly differential systems whose solutions can be expressed as linear combinations of {1, x, exp μx , exp −μx }, μ ∈ C, while the last stage of this method integrates exactly systems whose solutions are linear combinations of ...