Existence of almost periodic solutions of systems of linear and quasilinear differential equations with time lag
Existence of approximate solution to abstract nonlocal Cauchy problem.
Existence results for systems of conformable fractional differential equations
In this article, we study the existence of solutions to systems of conformable fractional differential equations with periodic boundary value or initial value conditions. where the right member of the system is -carathéodory function. We employ the method of solution-tube and Schauder’s fixed-point theorem.
Existence results for systems with nonlinear coupled nonlocal initial conditions
The purpose of the present paper is to study the existence of solutions to initial value problems for nonlinear first order differential systems subject to nonlinear nonlocal initial conditions of functional type. The approach uses vector-valued metrics and matrices convergent to zero. Two existence results are given by means of Schauder and Leray-Schauder fixed point principles and the existence and uniqueness of the solution is obtained via a fixed point theorem due to Perov. Two examples are...
Explicit two-step Runge-Kutta methods
The explicit two-step Runge-Kutta (TSRK) formulas for the numerical solution of ordinary differential equations are analyzed. The order conditions are derived and the construction of such methods based on some simplifying assumptions is described. Order barriers are also presented. It turns out that for order the minimal number of stages for explicit TSRK method of order is equal to the minimal number of stages for explicit Runge-Kutta method of order . Numerical results are presented which...
Exponential Multistep Methods for Ordinary Differential Equations
Extension of the method of quasilinearization for stochastic initial value problems.
Extrapolation at Stiff Differential Equations.
Extremal property of the equation
Familles de branches de bifurcations dans les équations de Ginzburg-Landau
Fifth-order Runge-Kutta with higher order derivative approximations.
Finding Liouvillian first integrals of rational ODEs of any order in finite terms.
Flows and diffeomorphisms.
Fundamental quadratic splines and applications
Further generalization of generalized quasilinearization method.
General linear methods: connection to one step methods and invariant curves.
Generalized differential equations in the space of regulated functions (boundary value problems and controllability)
Boundary value problems for generalized linear differential equations and the corresponding controllability problems are dealt with. The adjoint problems are introduced in such a way that the usual duality theorems are valid. As a special case the interface boundary value problems are included. In contrast to the earlier papers by the author the right-hand side of the generalized differential equations as well as the solutions of this equation can be in general regulated functions (not necessarily...
Global error control for the continuous Galerkin finite element method for ordinary differential equations
Global existence and asymptotic behavior of solution of second-order nonlinear impulsive differential equations.
Global stability of steady solutions for a model in virus dynamics
We consider a simple model for the immune system in which virus are able to undergo mutations and are in competition with leukocytes. These mutations are related to several other concepts which have been proposed in the literature like those of shape or of virulence – a continuous notion. For a given species, the system admits a globally attractive critical point. We prove that mutations do not affect this picture for small perturbations and under strong structural assumptions. Based on numerical...