A simple differential game.
Necessary and sufficient conditions for optimal strategies for differential /two person zero-sum/ game with sum determined by ordinary differential equations
Leitmann, G.↗
SEARCH · Search NASA
Results for “Differentiation”
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Semi-groups, groups and Lyapunov stability of partial differential equations.
Semigroups, groups and Liapunov stability of partial differential equation, obtaining operator differential equations in Hilbert spaces
Buis, G. R.↗
Variable-mesh method of solving differential equations
Multistep predictor-corrector method for numerical solution of ordinary differential equations retains high local accuracy and convergence properties. In addition, the method was developed in a form conducive to the generation of effective criteria for the selection of subsequent step sizes in step-by-step solution of differential equations.
Van Wyk, R.↗
On a class of differential games.
Two player zero-sum differential games with emphasis on play with state determined by differential equations, noting optimal solutions
Leitmann, G.↗
Functional differential equations
Functional class of differential-difference, retard differential, and difference equations
Hale, J. K.↗
On the uniform asymptotic stability of functional differential equations of the neutral type
Linear neutral differential equation uniform asymptotic stability relation to perturbed differential equation containing bounded linear operators
Hale, J. K.↗
Pulsed differential holographic measurements of vibration modes of high temperature panels
Holography is a lensless imaging technique which can be applied to measure static or dynamic displacements of structures. Conventional holography cannot be readily applied to measure vibration modes of high-temperature structures, due to difficulties caused by thermal convection currents. The present report discusses the use of pulsed differential holography, which is a technique for recording structural motions in the presence of random fluctuations such as turbulence. An analysis of the differential method is presented, and demonstration experiments were conducted using heated stainless steel plates. Vibration modes were successfully recorded for the heated plates at temperatures of 1000, 1600, and 2000 F. The technique appears promising for such future measurments as vibrations of the space shuttle TPS panels or recording flutter of aeroelastic models in a wind-tunnel.
Evensen, D. A.↗
Some efficient methods for obtaining infinite series solutions of n-th order linear ordinary differential equations
The use of the theta-operator method and generalized hypergeometric functions in obtaining solutions to nth-order linear ordinary differential equations is explained. For completeness, the analysis of the differential equation to determine whether the point of expansion is an ordinary point or a regular singular point is included. The superiority of the two methods shown over the standard method is demonstrated by using all three of the methods to work out several examples. Also included is a compendium of formulae and properties of the theta operator and generalized hypergeometric functions which is complete enough to make the report self-contained.
Allen, G.↗
Numerical method for the solution of large systems of differential equations of the boundary layer type
A numerical method for the solution of large systems of nonlinear differential equations of the boundary-layer type is described. The method is a modification of the technique for satisfying asymptotic boundary conditions. The present method employs inverse interpolation instead of the Newton method to adjust the initial conditions of the related initial-value problem. This eliminates the so-called perturbation equations. The elimination of the perturbation equations not only reduces the user's preliminary work in the application of the method, but also reduces the number of time-consuming initial-value problems to be numerically solved at each iteration. For further ease of application, the solution of the overdetermined system for the unknown initial conditions is obtained automatically by applying Golub's linear least-squares algorithm. The relative ease of application of the proposed numerical method increases directly as the order of the differential-equation system increases. Hence, the method is especially attractive for the solution of large-order systems. After the method is described, it is applied to a fifth-order problem from boundary-layer theory.
Green, M. J.↗
Observations of low-energy /0.3- to 1.8-MeV/ differential spectrums of trapped protons.
Measurements of differential energy spectrums of trapped protons obtained from several passes during the period January to November 1969 using the polar orbiting, low-altitude Injun 5 satellite equipped with a special solid-state detector proton-electron telescope are presented. Results reveal the existence of a quasi-persistent peak in the differential energy spectrum in the McIlwain shell parameter (L) range 2 to 2.6 and in the energy range of approximately 0.32 to 0.72 MeV. The fact that the shape of the spectrum is stable for several days or can change with time scales as small as 4 hours suggests an impulsive acceleration mechanism deep in the radiation belts. Other features of the spectrum show that if the spectrum is represented by an exponential form in energy, the dependence of the spectral parameter is in general agreement with diffusion theory over the L range of approximately 2 to 4.
Venkatesan, D.↗
New half-range differential approximation for spherically-symmetric radiative transfer.
A new half-range differential approximation for radiative transfer with spherical symmetry is presented. The development is motivated by the various failures of existing differential approximations in determining emissive-power distributions and heat transfer for concentric-spheres problems. The new approach represents a modification of the four-moment double spherical-harmonics method, to which it reduces in the planar limit. The difference is effected by relocating the discontinuity of the assumed directional distribution of radiation intensity. The shift takes the discontinuity from precisely on the division between radially inward and radially outward, to just within the radially-outward directional half range. The method is tested on a variety of concentric spheres problems with and without internal heat sources, reproducing all the important features of the exact results.
Moreno, J. B.↗
Measurement of differential atomic collision cross sections.
An apparatus for the study of differential angular scattering of atomic projectiles by gas targets is described. The design facilitates system alignment and provides for accurate reproducible location of components. The performance of the instrument is studied for scattering of H+ at 5-25 keV energies by helium and argon targets. Differential cross sections for elastic scattering and charge transfer are presented as well as total charge transfer cross sections. The coefficients for secondary electron ejection by impact of H and H+ on a metal surface are compared.
Fitzwilson, R. L.↗
Similarity and generalized finite-difference solutions of parabolic partial differential equations.
Techniques are presented for obtaining generalized finite-difference solutions to partial differential equations of the parabolic type. It is shown that the advantages of similarity in the solution of similar problems are generally not lost if the solution to the original partial differential equations is effected in the physical plane by finite-difference methods. The analysis results in a considerable saving in computational effort in the solution of both similar and nonsimilar problems. Several examples, including both the heat-conduction equation and the boundary-layer equations, are given. The analysis also provides a practical means of estimating the accuracy of finite-difference solutions to parabolic equations.
Clausing, A. M.↗
Differential geometric methods in system theory.
Discussion of certain problems in system theory which have been or might be solved using some basic concepts from differential geometry. The problems considered involve differential equations, controllability, optimal control, qualitative behavior, stochastic processes, and bilinear systems. The main goal is to extend the essentials of linear theory to some nonlinear classes of problems.
Brockett, R. W.↗
Similarity analysis of differential equations by Lie group.
Methods for transforming partial differential equations into forms more suitable for analysis and solution are investigated. The idea of Lie's infinitesimal contact transformation group is introduced to develop a systematic method which involves mostly algebraic manipulations. A thorough presentation of the application of this general method to the problem of similarity analysis in a broader sense - namely, the similarity between partial and ordinary differential equations, boundary value and initial value problems, and nonlinear and linear equations - is given with new and very general methods evolved for deriving the possible groups of transformations.
Na, T. Y.↗
Local behavior of autonomous neutral functional differential equations.
Basic problems for a special class of neutral functional differential equations (NFDE) are formulated, and some contributions to a general qualitative theory in the neighborhood of an equilibrium point are indicated. The properties of a NFDE (G,f) are examined to determine in what sense these properties are insensitive to small changes in (G,f) in the topology G x F. The special class of equations that is introduced includes retarded functional differential equations and difference equations.
Hale, J. K.↗
Lie algebras and linear differential equations.
Certain symmetry properties possessed by the solutions of linear differential equations are examined. For this purpose, some basic ideas from the theory of finite dimensional linear systems are used together with the work of Wei and Norman on the use of Lie algebraic methods in differential equation theory.
Brockett, R. W.↗
Four-phase differential phase shift resolver
Two systems have been developed to resolve phase uncertainty without transmitting reference signals. In both methods signal is impressed on carrier as differential, rather than absolute, phase shift. At the receiver four-phase demodulation and logic process unambiguously resolves differential phase shift of input carrier.
Hopkins, P. M.↗