Lie Series Solutions of Partial Differential Equations Final Report, 1 Jul. 1965 - 31 Jul. 1966
Application of Lie series to solution of linear ordinary differential equations of second order
PROBLEM SOLVING↗
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Stability criteria for n-th order, homogeneous linear differential equations
Stability criteria for n-th order homogeneous linear differential equations for real continuous functions obtained by Liapunov method
LIAPUNOV FUNCTION↗
Study of perturbed periodic systems of differential equations - The Stroboscopic method
Stroboscopic method for solving perturbed periodic systems of differential equations
DIFFERENTIAL EQUATION↗
Solution of ordinary differential equations by means of Lie series
Solution of ordinary differential equations by Lie series - Laplace transformation, Weber parabolic-cylinder functions, Helmholtz equations, and applications in physics
DIFFERENTIAL EQUATION↗
The solution of the general homogeneous linear differential equation of second order
Solution of general homogenous linear differential equation of second order using Lie groups
DIFFERENTIAL EQUATION↗
The solution of the general inhomogeneous linear differential equation of second order
Solution of general inhomogenous linear differential equations of second order using Lie groups
DIFFERENTIAL EQUATION↗
On the Solution of the Differential Equations Resulting from the Separation of Laplace Equation in Various Coordinate Systems, by Means of Lie Series Scientific Report No. 9
Solution of differential equations resulting from separation of Laplace equation in various coordinate systems
COORDINATE SYSTEM↗
An engineering expose of numerical integration of ordinary differential equations
Error analyses for numerically integrating first order ordinary differential equations
NUMERICAL INTEGRATION↗
Sufficient conditions for stability and instability of autonomous functional- Differential equations.
Liapunov function determining sufficient conditions for stability of autonomous functional differential equations with finite time lag
DIFFERENTIAL EQUATION↗
Some applications of stochastic differential equations to optimal nonlinear filtering.
Stochastic differential equations specifying dynamical structure of filters generating posterior probability distribution when inputs are time functions
PROBABILITY DISTRIBUTION↗
Solutions of differential equations by evaluations of functions.
Runge-Kutta fourth order formula used to obtain approximate solution to differential equations
RUNGE-KUTTA INTEGRATION↗
Averaging methods for differential equations with retarded arguments and a small parameter.
Averaging method for differential equations with retarded arguments
PERTURBATION THEORY↗
Second order ordinary differential operators with general boundary conditions.
General boundary conditions for second-order ordinary differential operators
BOUNDARY VALUE↗
The condition of regular degeneration for singularly perturbed systems of linear differential-difference equations.
Extension of problem of singular perturbation for linear scalar constant coefficient differential- difference equation with single retardation to several retardations, noting degenerate equation solution
LINEAR EQUATION↗
An experimental determination of differential equations to describe simple nonlinear systems.
Ordinary differential equations experimentally determined for describing performance of existing lumped-parameter time-invariant nonlinear physical systems
NONLINEAR SYSTEM↗
Concerning the numerical solution of differential equations.
Step size for numerical solution of differential equation without violating stability region constraint
DIFFERENTIAL EQUATION↗
Calculation of subdominant solutions of linear differential equations.
Subdominant solutions of linear differential equations calculated by numerical method
NUMERICAL INTEGRATION↗
On discretization and differentiation of operators with application to Newton's method.
Discretization and differentiation of operators with commutativity proof and with application to Newton method
DIFFERENTIAL OPERATOR↗