منابع مشابه
Preconditioning of implicit Runge-Kutta methods
A major problem in obtaining an efficient implementation of fully implicit RungeKutta (IRK) methods applied to systems of differential equations is to solve the underlying systems of nonlinear equations. Their solution is usually obtained by application of modified Newton iterations with an approximate Jacobian matrix. The systems of linear equations of the modified Newton method can actually b...
متن کاملValidated Explicit and Implicit Runge-Kutta Methods∗†
A set of validated numerical integration methods based on explicit and implicit Runge-Kutta schemes is presented to solve, in a guaranteed way, initial value problems of ordinary differential equations. Runge-Kutta methods are well-known to have strong stability properties, which make them appealing to be the basis of validated numerical integration methods. A new approach to bound the local tr...
متن کاملImplicit Runge-Kutta Methods for Orbit Propagation
Accurate and efficient orbital propagators are critical for space situational awareness because they drive uncertainty propagation which is necessary for tracking, conjunction analysis, and maneuver detection. We have developed an adaptive, implicit Runge-Kuttabased method for orbit propagation that is superior to existing explicit methods, even before the algorithm is potentially parallelized....
متن کاملImplicit Runge-kutta Methods for Uncertainty Propagation
Accurate and efficient orbital propagators are critical for space situational awareness because they drive uncertainty propagation which is necessary for tracking, conjunction analysis, and maneuver detection. Existing sigma pointor particle-based methods for uncertainty propagation use explicit numerical integrators for propagating the closely spaced orbital states as part of the prediction st...
متن کاملBandlimited implicit Runge–Kutta integration for Astrodynamics
We describe a new method for numerical integration, dubbed bandlimited collocation implicit Runge–Kutta (BLC-IRK), and compare its efficiency in propagating orbits to existing techniques commonly used in Astrodynamics. The BLC-IRK scheme uses generalized Gaussian quadratures for bandlimited functions. This new method allows us to use significantly fewer force function evaluations than explicit ...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1964
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1964-0159424-9