Center manifold and exponentially-bounded solutions of a forced Newtonian system with dissipation.
Classification analytique des équations différentielles non linéaires résonnantes du premier ordre
Collocation methods for differential-algebraic equations of index 3.
Common increasing dispersions of certain linear second order differential equations
Comparing the radii of some balls appearing in connection to three local convergence theorems for Newton's method.
Computing the differential of an unfolded contact diffeomorphism
Consider a bifurcation problem, namely, its bifurcation equation. There is a diffeomorphism linking the actual solution set with an unfolded normal form of the bifurcation equation. The differential of this diffeomorphism is a valuable information for a numerical analysis of the imperfect bifurcation. The aim of this paper is to construct algorithms for a computation of . Singularity classes containing bifurcation points with , are considered.
Conditions for the integrability of a second order nonlinear differential equation.
Consensus of a two-agent system with nonlinear dynamics and time-varying delay
To explore the impacts of time delay on nonlinear dynamics of consensus models, we incorporate time-varying delay into a two-agent system to study its long-time behaviors. By the classical 3/2 stability theory, we establish a sufficient condition for the system to experience unconditional consensus. Numerical examples show the effectiveness of the proposed protocols and present possible Hopf bifurcations when the time delay changes.
Construction of interval wavelet based on restricted variational principle and its application for solving differential equations.
Continuability, boundedness, and convergence to zero of solutions of a perturbed nonlinear ordinary differential equation
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 Properties of the Runge-Kutta-Chebyshev Method.
Corrigendum to: Positive solutions for systems of generalized three-point nonlinear boundary value problems
Critical point theory and nonlinear differential equations
Cubic and quartic planar differential systems with exact algebraic limit cycles.