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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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Solution of second order differential equation of hyperbolic type by reduction to system of integral equations
Solution of differential equations resulting from separation of Laplace equation in various coordinate systems
Lie group use in solution of equations resulting from separation of Helmholtz equations in special coordinate systems
Maxwell field equations and constitutive equations, discussing best pedagogical formulation for electrodynamics
Linear Fokker-Planck equation describing Brownian motion from kinetic equation for weakly interacting gases
Volterra and partial differential equations solution asymptotic behavior treated, indicating connection to boundary problems in parabolic equations and optimal control
Wave equation in quarter space, showing particular solution of Laplace equation with wave velocity increase
Reducing differential equations of viscous shock layer to boundary layer equations
Liapunov functions from auxiliary exact difference equations for nonlinear difference equation stability analysis
Localization of linear integral equation eigenvalues with applications to linear ordinary differential equations
Difference equations for approximating ordinary differential equations
Basic formulations for developing coordinate transformations and motion equations used with free-flight and wind-tunnel data reduction are presented. The general forms presented include axes transformations that enable transfer back and forth between any of the five axes systems that are encountered in aerodynamic analysis. Equations of motion are presented that enable calculation of motions anywhere in the vicinity of the earth. A bibliography of publications on methods of analyzing flight data is included.
The equivalence of a considered integral equation form with an infinite system of linear equations is proved, and the localization of the eigenvalues of the infinite system is expressed. Error estimates are derived, and the problems of finding upper bounds and lower bounds for the eigenvalues are solved simultaneously.
An integral equation method for solving the full potential equation has been developed for arbitrary configurations in two- or three-dimensional transonic flows. This method is capable of capturing shocks using Murman-Cole type of finite difference scheme and is capable of predicting accurate and force-free wake shape as well. A rectangular grid combined with a technique of local grid refinement greatly improved the computational efficiency.
New shock-capturing finite difference approximations for solving two scalar conservation law nonlinear partial differential equations describing inviscid, isentropic, compressible flows of aerodynamics at transonic speeds are presented. A global linear stability theorem is applied to these schemes in order to derive a necessary and sufficient condition for the finite element method. A technique is proposed to render the described approximations total variation-stable by applying the flux limiters to the nonlinear terms of the difference equation dimension by dimension. An entropy theorem applying to the approximations is proved, and an implicit, forward Euler-type time discretization of the approximation is presented. Results of some numerical experiments using the approximations are reported.
Liapunov stability theory applied to class of partial differential equations, and generation of contraction groups related to equivalent norms
Dynamic equations for simulating multiple-bodied spacecraft configuration subjected to gravity gradient and disturbance torques and forces
Equations for active control system of generalized spacecraft simulation computer program