Critical cases for neutral functional differential equations
Neutral functional equation including scalar differential-difference equation, determining sufficient conditions for zero solution
Hale, J. K.↗
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Results for “differential equations”
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Convergence of step-by-step methods for non-linear integro-differential equations.
The theory of consistent step-by-step methods for solving Volterra integral equations is extended to nonsingular Volterra integro-differential equations. It is shown that standard step-by-step algorithms for these more general equations are convergent. Several numerical examples are included.
Mocarsky, W. L.↗
On the construction of highly stable, explicit, numerical methods for integrating coupled ordinary differential equations with parasitic eigenvalues
Explicit numerical methods for integrating coupled nonlinear ordinary differential equations with parasitic eignevalues
Lomax, H.↗
Perturbation of solutions of differential equations satisfying general boundary conditions
Perturbation of solutions of system of nonlinear differential equations under general linear boundary conditions
Lewis, D. C.↗
Periodic solutions of differential equations with time lag containing a small parameter.
Periodic solutions for functional differential equations with time lag, developing bifurcation theory representing delay equation extension
Perello, C.↗
Numerical integration of ordinary differential equations of various orders
Report describes techniques for the numerical integration of differential equations of various orders. Modified multistep predictor-corrector methods for general initial-value problems are discussed and new methods are introduced.
Gear, C. W.↗
Bibliography on techniques for solving partial differential equations by hybrid computation and other methods
Parabolic, elliptic, and hyperbolic partial differential equations using analog and hybrid methods - bibliographies
Finn, D. L.↗
Probability limit theorems and the convergence of finite difference approximations of partial differential equations
Probability limit theorems and convergence of finite difference approximations of partial differential equations
Kushner, H. J.↗
Accelerating convergence of one-step methods for the numerical solution of ordinary differential equations.
Accelerating convergence of one step methods for numerical solution of ordinary differential equations, discussing various initial value problems
Waddell, E. R.↗
The classification of partial differential equations in structural dynamics.
Classification of second order quasi-linear partial differential equations with two independent variables in structural dynamics with emphasis on elastic structures
Chou, P. C.↗
Functional differential equations
Functional class of differential-difference, retard differential, and difference equations
Hale, J. K.↗
Conditions for the existence of conjugate points for a fourth order linear differential equation
Existence conditions of conjugate points for nontrivial solution of fourth order differential equation
Bradley, J. S.↗
Random differential equations in control theory
Control processes and optimization problems solutions by stochastic differential equations, discussing dynamic models and programming, linear filtering and optimal feedback
Wonham, W. M.↗
Behavior near a periodic orbit of functional differential equations
Equilibrium points and periodic orbits, using qualitative theory of autonomous functional differential equations
Hale, J. K.↗
Second-order non-iterative ADI solution of non-linear partial differential equations
A new method for the solution of non-linear partial differential equations by an ADI procedure is described. Although the method is second order accurate in time, it does not require either iterations or predictor corrector methods to overcome the nonlinearity of the equations. Thus the computational effort required for the solution of the non-linear problem becomes similar to that required for the linear case. The method is applied to a two-dimensional 'extended Burgers equation'. Linear stability is studied, and some numerical solutions obtained. The improved accuracy obtained by the 2nd order truncation error is clearly manifested.
Wolfshtein, M.↗
Error propagation in the numerical solutions of the differential equations of orbital mechanics
The relationship between the eigenvalues of the linearized differential equations of orbital mechanics and the stability characteristics of numerical methods is presented. It is shown that the Cowell, Encke, and Encke formulation with an independent variable related to the eccentric anomaly all have a real positive eigenvalue when linearized about the initial conditions. The real positive eigenvalue causes an amplification of the error of the solution when used in conjunction with a numerical integration method. In contrast an element formulation has zero eigenvalues and is numerically stable.
Bond, V. R.↗
A Solution to the Fundamental Linear Fractional Order Differential Equation
This paper provides a solution to the fundamental linear fractional order differential equation, namely, (sub c)d(sup q, sub t) + ax(t) = bu(t). The impulse response solution is shown to be a series, named the F-function, which generalizes the normal exponential function. The F-function provides the basis for a qth order "fractional pole". Complex plane behavior is elucidated and a simple example, the inductor terminated semi- infinite lossy line, is used to demonstrate the theory.
Hartley, Tom T.↗
Probability Limit Theorems and the Convergence of Finite Difference Approximations of Partial Differential Equations
Probability limit theorems applied to convergence of finite difference approximations of partial differential equations
Kushner, H. J.↗