Numerical integration of nonlinear differential equations by use of rational approximation Final report, 15 Jan. 1965 - 14 Jul. 1967
Numerical integration of nonlinear differential equations by use of rational approximation
NUMERICAL INTEGRATION↗
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Application of group and transformation theory to the solution of ordinary and partial differential equations Final report
Lie transformation group for solution of partial differential equations
Driskell, C. N., Jr.↗
Hybrid-computer Monte Carlo techniques for finding eigenvalues of partial differential equations
Monte Carlo method for estimating eigenvalues of elliptical partial differential equations
Daquanni, R.↗
Simplification of second order systems of ordinary differential equations with a turning point.
Reduction theorem for second order differential equations with turning point involving simultaneous change of dependent/independent variables and matrix equation solution
Hanson, R. J.↗
Variable mesh methods for differential equations
Variable mesh multistep methods for numerical solution of nonlinear differential equations
Van Wyk, R.↗
A local existence theorem for quasi-linear partial differential equations
Sufficient conditions for solutions of quasi-linear partial differential equation
Artiaga, L.↗
A generalized averaging method for linear differential equations with almost periodic coefficients
Generalized averaging method for linear differential equations with almost periodic coefficients
Coakley, T. J.↗
Simplification of second order systems of ordinary differential equations with a turning point.
Second order systems of linear differential equations eliminating all nonessential difficulties associated with initial value problem
Hanson, R. J.↗
Hyperbolic differential equations in two dimensions.
General two dimensional second order hyperbolic differential equation analyzed by substitution method
Kundt, W.↗
Semi-groups, groups and Lyapunov stability of partial differential equations
Applications of group theory and Liapunov stability to partial differential equations
Buis, G. R.↗
Exponential estimates and the saddle point property for neutral functional differential equations
Exponential estimates and saddle point property for neutral functional differential equations
Cruz, M. A.↗
On the uniform asymptotic stability of functional differential equations of the neutral type
Uniform asymptotic stability of functional differential equations of neutral type
Hale, J. K.↗
On the stability of nonlinear operator differential equations, and applications
Existence and stability problems of nonlinear operator differential equations containing linear operator with domain and range contained in real Hilbert space
Pao, C. V.↗
Power series solutions of ordinary differential equations in MACSYMA
A program is described which extends the differential equation solving capability of MACSYMA to power series solutions and is available via the SHARE library. The program is directed toward those classes of equations with variable coefficients (in particular, those with singularities) and uses the method of Frobenius. Probably the most important distinction between this package and others currently available or being developed is that, wherever possible, this program will attempt to provide a complete solution to the equation rather than an approximation, i.e., a finite number of terms. This solution will take the form of a sum of infinite series.
Lafferty, E. L.↗
The method of averages applied to the KS differential equations
A new approach for the solution of artificial satellite trajectory problems is proposed. The basic idea is to apply an analytical solution method (the method of averages) to an appropriate formulation of the orbital mechanics equations of motion (the KS-element differential equations). The result is a set of transformed equations of motion that are more amenable to numerical solution.
Graf, O. F., Jr.↗
Numerical methods for large-scale, time-dependent partial differential equations
A survey of numerical methods for time dependent partial differential equations is presented. The emphasis is on practical applications to large scale problems. A discussion of new developments in high order methods and moving grids is given. The importance of boundary conditions is stressed for both internal and external flows. A description of implicit methods is presented including generalizations to multidimensions. Shocks, aerodynamics, meteorology, plasma physics and combustion applications are also briefly described.
Turkel, E.↗
The use of solution adaptive grids in solving partial differential equations
The grid point distribution used in solving a partial differential equation using a numerical method has a substantial influence on the quality of the solution. An adaptive grid which adjusts as the solution changes provides the best results when the number of grid points available for use during the calculation is fixed. Basic concepts used in generating and applying adaptive grids are reviewed in this paper, and examples illustrating applications of these concepts are presented.
Anderson, D. A.↗
Spectral methods for time dependent partial differential equations
The theory of spectral methods for time dependent partial differential equations is reviewed. When the domain is periodic Fourier methods are presented while for nonperiodic problems both Chebyshev and Legendre methods are discussed. The theory is presented for both hyperbolic and parabolic systems using both Galerkin and collocation procedures. While most of the review considers problems with constant coefficients the extension to nonlinear problems is also discussed. Some results for problems with shocks are presented.
Gottlieb, D.↗