On the Accumulation of Errors at Numerical Integration in Some Problems of Celestial Mechanics
Accumulation of errors using numerical integration methods for solving celestial equations of motion
MOTION EQUATION↗
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An operational unification of finite difference methods for the numerical integration of ordinary differential equations
Operational unification of finite difference methods for numerical integration of ordinary differential equations
FINITE DIFFERENCE METHOD↗
Numerical integration of orbits in multirevolution steps
Predictor-corrector algorithm applicable to numerical integration of satellite orbits in multirevolution steps
SATELLITE ORBIT↗
A critical analysis of various numerical integration methods for computing the flow of a gas in chemical nonequilibrium
Numerical integration methods for computing flow of gas in chemical nonequilibrium behind normal shock wave
NONEQUILIBRIUM FLOW↗
Cowell type numerical integration as applied to satellite orbit computation
Cowell numerical integration and satellite orbit calculation
Maury, J. L., Jr.↗
Numerical integration orbits and Brouwer and modified Brouwer orbits
Numerical integration orbits and Brouwer and modified Brouwer orbits
Hertz, H. G.↗
Estimating numerical integration errors
Algorithm for use in estimating accumulated numerical integration errors
Arldt, M. J.↗
Error analysis of numerical integration schemes
Digital simulation for error analysis of numerical integration schemes
Source record↗
Analysis of error growth and stability for the numerical integration of the equations of chemical kinetics
Error growth and stability analyzed for numerical integration of differential equations in chemical kinetics
NUMERICAL INTEGRATION↗
A method for the numerical integration of coupled first-order differential equations with greatly different time constants.
Numerical integration of coupled first order ODE OF greatly differing time constant
DIFFERENTIAL EQUATION↗
Comparison theorems, numerical integration and satellite orbits
A comparison theorem estimating the difference between solutions of a perturbed and unperturbed equation is obtained. This is then applied to obtain error estimates in numerical integration problems, in particular, those problems involving computation of satellite orbits. The main result is a proof of the intuitive notion that the error in numerically integrating a stable equation grows less rapidly than for an unstable equation.
Stokes, A.↗
On the application of difference methods for the asymptotic estimates of errors at numerical integration of systems of ordinary differential equations
Difference methods for asymptotic estimates of errors at numerical integration of systems of ordinary differential equations
NUMERICAL INTEGRATION↗
An application of group theory to the numerical integration of the equations of motion of a conservative dynamical system
Application of group theory to numerical integration of motion equations of conservative dynamical system
NUMERICAL INTEGRATION↗
The application of a numerical integration procedure developed by erwin fehlberg to the restricted problem of three bodies
Application of numerical integration procedures to restricted three-body problem
THREE-BODY PROBLEM↗
Self-starting procedure simplifies numerical integration
A self-starting, multistep procedure for the numerical integration of ordinary differential equations is devised to produce all the required backward differences directly from the initial equations. The self-starting element eliminates nonessential tallying to determine starting values.
Source record↗
Analysis of numerical integration techniques for real-time digital flight simulation
Numerical integration techniques for real time digital flight simulation
Steinmetz, G. G.↗
Special Perturbations Using Back-Correction Methods of Numerical Integration
A new class of linear multistep methods for numerical integration of differential equations is reported that permits satellite computation solutions to be corrected at certain points in the past as the integration advances in time. Algorithms have been developed for the solution of both first- and second-order differential equations. The back correction method appears to be more efficient than classical methods when dominant and perturbing forces can be separated.
Feagin, T.↗
Orientation of the earth by numerical integration
A fundamental problem is the determination of the orientation of the earth in the celestial coordinate system. Classical reductions for precession and nutation can be expected to be consistent with the present-day observations, however, corrections to the classical theory are difficult to model because of the large number of coefficients involved. Consequently, a portion of the research has been devoted to numerically integrating the Eulerian equations of motion for a rigid earth and considering the six initial conditions of the integration as unknowns. Comparison of the three adjusted Eulerian angles from the numerical integration over 1000 days indicates agreement with classical theory to within 0.003 seconds of arc.
Fajemirokun, F. A.↗