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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Classical eight- and lower-order Runge-Kutta-Nystroem formulas with stepsize control for special second-order differential equations

The formulas include a stepsize control procedure, based on a complete coverage of the leading term of the truncation error in x. The formulas require fewer evaluations per stop than other Runge-Kutta-Nystrom formulas if the latter are operated by using the standard procedure for stepsize control. An example is presented. With results being of the same accuracy, Runge-Kutta-Nystrom formulas discussed save 50 percent or more computer time compared with other Runge-Kutta-Nystrom formulas.

Fehlberg, E.↗
NASA NTRS1975

New methods for the numerical integration of ordinary differential equations and their application to the equations of motion of spacecraft

A number of hybrid methods for solving Cauchy problems are described on the basis of an evaluation of advantages of single and multiple-point numerical integration methods. The selection criterion is the principle of minimizing computer time. The methods discussed include the Nordsieck method, the Bulirsch-Stoer extrapolation method, and the method of recursive Taylor-Steffensen power series.

Banyukevich, A.↗
NASA NTRS1974

Reanalysis information for eigenvalues derived from a differential equation analysis formulation

The investigation reported demonstrates that in the case considered perturbation methods can be used in a straightforward manner to obtain reanalysis information. A perturbation formula for the buckling loads of a general shell of revolution is derived. The accuracy of the obtained relations and their range of application is studied with the aid of a specific example involving a particular stiffened shell of revolution.

Thornton, W. A.↗
NASA NTRS1976

Atmospheric temperature profiles derived through the inversion of a system of first order differential equations

Generation of vertical temperatures profiles from remotely sensed atmospheric radiance data is described as an analogous communications system. The radiative transport characteristics of the atmosphere encodes the continuous temperature profile into an 'n' element vector where 'n' is the number of channels in the satellite instrument. The temperature profile is a message transmitted from station A to station B and the link is the satellite instrument. At station B the decoder reproduces a continuous function which is the best estimate of the message encoded at station A. It is shown that the decoder must operate in a tuned mode where the parameters used in the encoder precisely determine the decoder parameters, and that the characteristics of the total message block must be given by a set of decoder constraints

Gatlin, J. A.↗
NASA NTRS1977

Simplified clustering of nonorthogonal grids generated by elliptic partial differential equations

A simple clustering transformation is combined with the Thompson, Thames, and Mastin (TTM) method of generating computational grids to produce controlled mesh spacings. For various practical grids, the resulting hybrid scheme is easier to apply than the inhomogeneous clustering terms included in the TTM method for this purpose. The technique is illustrated in application to airfoil problems, and listings of a FORTRAN computer code for this usage are included.

Sorenson, R. L.↗
NASA NTRS1978

On several aspects and applications of the multigrid method for solving partial differential equations

Several aspects of multigrid methods are briefly described. The main subjects include the development of very efficient multigrid algorithms for systems of elliptic equations (Cauchy-Riemann, Stokes, Navier-Stokes), as well as the development of control and prediction tools (based on local mode Fourier analysis), used to analyze, check and improve these algorithms. Preliminary research on multigrid algorithms for time dependent parabolic equations is also described. Improvements in existing multigrid processes and algorithms for elliptic equations were studied.

Dinar, N.↗
NASA NTRS1978

The stability of numerical methods for second order ordinary differential equations

An important characterization of a numerical method for first order ODE's is the region of absolute stability. If all eigenvalues of the linear problem dy/dt = Ay are inside this region, the numerical method is stable. If the second order system d/dt(dy/dt) = 2Ady/dt - By is solved as a first order system, the same result applies to the eigenvalues of the generalized eigenvalue problem (lambda-squared)I 2(lambda)A + B. No such region exists for general methods for second order equations, but in some cases a region of absolute stability can be defined for methods for the single second order equation d/dt(dy/dt) = 2ady/dt - by. The absence of a region of absolute stability can occur when different members of a system of first order equations are solved by different methods.

Gear, C. W.↗
NASA NTRS1973

Program for the solution of multipoint boundary value problems of quasilinear differential equations

Linear equations are solved by a method of superposition of solutions of a sequence of initial value problems. For nonlinear equations and/or boundary conditions, the solution is iterative and in each iteration a problem like the linear case is solved. A simple Taylor series expansion is used for the linearization of both nonlinear equations and nonlinear boundary conditions. The perturbation method of solution is used in preference to quasilinearization because of programming ease, and smaller storage requirements; and experiments indicate that the desired convergence properties exist although no proof or convergence is given.

Source record↗
NASA NTRS1979

Lyapunov stability and its application to systems of ordinary differential equations

An outline and a brief introduction to some of the concepts and implications of Lyapunov stability theory are presented. Various aspects of the theory are illustrated by the inclusion of eight examples, including the Cartesian coordinate equations of the two-body problem, linear and nonlinear (Van der Pol's equation) oscillatory systems, and the linearized Kustaanheimo-Stiefel element equations for the unperturbed two-body problem.

Kennedy, E. W.↗
NASA NTRS1983

Stochastic differential equations and turbulent dispersion

Aspects of the theory of continuous stochastic processes that seem to contribute to an understanding of turbulent dispersion are introduced and the theory and philosophy of modelling turbulent transport is emphasized. Examples of eddy diffusion examined include shear dispersion, the surface layer, and channel flow. Modeling dispersion with finite-time scale is considered including the Langevin model for homogeneous turbulence, dispersion in nonhomogeneous turbulence, and the asymptotic behavior of the Langevin model for nonhomogeneous turbulence.

Durbin, P. A.↗
NASA NTRS1983

Finite difference numerical methods for boundary control problems governed by hyperbolic partial differential equations

This paper briefly reviews convergent finite difference schemes for hyperbolic initial boundary value problems and their applications to boundary control systems of hyperbolic type which arise in the modelling of vibrations. These difference schemes are combined with the primal and the dual approaches to compute the optimal control in the unconstrained case, as well as the case when the control is subject to inequality constraints. Some of the preliminary numerical results are also presented.

Chen, G.↗