Convergence of a mimetic finite difference method for static diffusion equation.
Convergence of Cohen-Grossberg neural networks with delays and time-varying coefficients.
Convergence of eigenfunction expansions corresponding to nonlinear Sturm-Liouville operators.
Convergence of formal solutions of first order singular partial differential equations of nilpotent type
Let (x,y,z) ∈ ℂ³. In this paper we shall study the solvability of singular first order partial differential equations of nilpotent type by the following typical example: , where . For this equation, our aim is to characterize the solvability on by using the Im P, Coker P and Ker P, and we give the exact forms of these sets.
Convergence of multistep methods for systems of ordinary differential equations with parameters
The author considers the convergence of quasilinear nonstationary multistep methods for systems of ordinary differential with parameters. Sufficient conditions for their convergence are given. The new numerical method is tested for two examples and it turns out to be a little better than the Hamming method.
Convergence of Multistep Methods for Volterra Functional Differential Equations.
Convergence of numerical methods for systems of neutral functional-differential-algebraic equations
A general class of numerical methods for solving initial value problems for neutral functional-differential-algebraic systems is considered. Necessary and sufficient conditions under which these methods are consistent with the problem are established. The order of consistency is discussed. A convergence theorem for a general class of methods is proved.
Convergence of solutions for a fifth-order nonlinear differential equation.
Convergence of solutions of certain fourth-order nonlinear differential equations.
Convergence of solutions of certain non-homogeneous third order ordinary differential equations
Convergence of the Lagrange-Newton method for optimal control problems
Convergence results for two Lagrange-Newton-type methods of solving optimal control problems are presented. It is shown how the methods can be applied to a class of optimal control problems for nonlinear ODEs, subject to mixed control-state constraints. The first method reduces to an SQP algorithm. It does not require any information on the structure of the optimal solution. The other one is the shooting method, where information on the structure of the optimal solution is exploited. In each case,...
Convergence of the solutions for the equation .
Convergence properties of the finite difference method for solving variational inequalities
Convergence Properties of the Runge-Kutta-Chebyshev Method.
Convergence rate of the solutions of singularly perturbed time-optimal control problems
Convergence results for nonlinear evolution inclusions
In this paper we consider evolution inclusions of subdifferential type. First, we prove a convergence result and a continuous dependence proposition for abstract Cauchy problem of the form u' ∈ -∂⁻f(u) + G(u), u(0) = x₀, where ∂⁻f is the Fréchet subdifferential of a function f defined on an open subset Ω of a real separable Hilbert space H, taking its values in IR ∪ {+∞}, and G is a multifunction from C([0,T],Ω) into the nonempty subsets of L²([0,T],H). We obtain analogous results for the multivalued...
Convergence tests for one scalar differential equation with vanishing delay
Convergence to equilibria in a differential equation with small delay
Convergence to equilibria in a differential equation with small delay
Consider the delay differential equation where is a constant and is Lipschitzian. It is shown that if is small, then the solutions of (1) have the same convergence properties as the solutions of the ordinary differential equation obtained from (1) by ignoring the delay.
Converse theorem for practical stability of nonlinear impulsive systems and applications
The Lyapunov's second method is one of the most famous techniques for studying the stability properties of dynamic systems. This technique uses an auxiliary function, called Lyapunov function, which checks the stability properties of a specific system without the need to generate system solutions. An important question is about the reversibility or converse of Lyapunov's second method; i. e., given a specific stability property does there exist an appropriate Lyapunov function? The main result of...