Speed and Accuracy Tests of the Variable-Step Stoermer-Cowell Integrator
نویسندگان
چکیده
The variable-step Störmer-Cowell integrator is a non-summed, double-integration multi-step integrator derived in variable-step form. The method has been implemented with a Shampine-Gordon style error control algorithm that uses an approximation of the local error at each step to choose the step size for the subsequent step. In this paper, the variable-step Störmer-Cowell method is compared to several other multi-step integrators, including the fixed-step Gauss-Jackson method, the Gauss-Jackson method with s-integration, and the variable-step single-integration ShampineGordon method, in both orbit propagation and orbit determination. The results show the variablestep Störmer-Cowell method is comparable with Gauss-Jackson using s-integration, except in high drag cases where the variable-step Störmer-Cowell method has an advantage in speed and accuracy.
منابع مشابه
A Variable-Step Double-Integration Multi-Step Integrator
A new method of numerical integration is presented here, the variable-step Störmer-Cowell method. The method uses error control to regulate the step size, so larger step sizes can be taken when possible, and is double-integration, so only one evaluation per step is necessary when integrating second-order differential equations. The method is not variable-order, because variable-order algorithms...
متن کاملPaper AAS 03-664 ACCURACY AND SPEED EFFECTS OF VARIABLE STEP INTEGRATION FOR ORBIT DETERMINATION AND PROPAGATION
In this paper the fixed step Gauss-Jackson method is compared to two variable step integrators. The first is the variable step, variable order Shampine-Gordon method. The second is s-integration, which may be considered an analytical step regulation. Speed tests are performed for orbit propagation with the integrators set to give equivalent accuracy. The integrators are also tested for orbit de...
متن کاملAAS 04-238 A Variable-Step Double-Integration Multi-Step Integrator
A variable-step double-integration multi-step integrator is derived using divided differences. The derivation is based upon the derivation of Shampine-Gordon, a single-integration method. Variable-step integrators are useful for propagating elliptical orbits, because larger steps can be taken near apogee. As a double-integration method, the integrator performs only one function evaluation per s...
متن کاملTime stepping N-body simulations
Leapfrog integration has been the method of choice in N-body simulations owing to its low computational cost for a symplectic integrator with second order accuracy. We introduce a new leapfrog integrator that allows for variable timesteps for each particle in large N-body simulations. Tests with single particles in fixed potentials show that it behaves as a symplectic integrator. We then examin...
متن کاملA Family of Variable Step-Size Normalized Subband Adaptive Filter Algorithms Using Statistics of System Impulse Response
This paper presents a new variable step-size normalized subband adaptive filter (VSS-NSAF) algorithm. The proposed algorithm uses the prior knowledge of the system impulse response statistics and the optimal step-size vector is obtained by minimizing the mean-square deviation(MSD). In comparison with NSAF, the VSS-NSAF algorithm has faster convergence speed and lower MSD. To reduce the computa...
متن کامل