Radial selfsimilar solutions of a nonlinear Ornstein-Uhlenbeck equation.
Raman laser : mathematical and numerical analysis of a model
In this paper we study a discrete Raman laser amplification model given as a Lotka-Volterra system. We show that in an ideal situation, the equations can be written as a Poisson system with boundary conditions using a global change of coordinates. We address the questions of existence and uniqueness of a solution. We deduce numerical schemes for the approximation of the solution that have good stability.
Raman laser: mathematical and numerical analysis of a model
In this paper we study a discrete Raman laser amplification model given as a Lotka-Volterra system. We show that in an ideal situation, the equations can be written as a Poisson system with boundary conditions using a global change of coordinates. We address the questions of existence and uniqueness of a solution. We deduce numerical schemes for the approximation of the solution that have good stability.
Rational Constants of Generic LV Derivations and of Monomial Derivations
We describe the fields of rational constants of generic four-variable Lotka-Volterra derivations. Thus, we determine all rational first integrals of the corresponding systems of differential equations. Such systems play a role in population biology, laser physics and plasma physics. They are also an important part of derivation theory, since they are factorizable derivations. Moreover, we determine the fields of rational constants of a class of monomial derivations.
Recent results concerning dynamic equations on time scales.
Reducibility and characterization of symplectic Runge-Kutta methods.
Regularly varying solutions of generalized Thomas-Fermi equations
Regulatory network of drug-induced enzyme production: parameter estimation based on the periodic dosing response measurement
The common goal of systems pharmacology, i.e. systems biology applied to the field of pharmacology, is to rely less on trial and error in designing an input-output systems, e.g. therapeutic schedules. In this paper we present, on the paradigmatic example of a regulatory network of drug-induced enzyme production, the further development of the study published by Duintjer Tebbens et al. (2019) in the Applications of Mathematics. Here, the key feature is that the nonlinear model in form of an ODE system...
Remark in connection with an article of G. G. Hamedani: “Global existence of solutions of certain functional-differential equations” [Časopis Pěst. Mat. 106 (1981), 48-51]
Remark to transformations of linear differential and functional-differential equations
For linear differential and functional-differential equations of the -th order criteria of equivalence with respect to the pointwise transformation are derived.
Remarks concerning Driver's equation
We consider uniqueness for the initial value problem x' = 1 + f(x) - f(t), x(0) = 0. Several uniqueness criteria are given as well as an example of non-uniqueness.
Remarks on multiple periodic solutions of nonlinear ordinary differential equations
Richardson Extrapolation combined with the sequential splitting procedure and the θ-method
Initial value problems for systems of ordinary differential equations (ODEs) are solved numerically by using a combination of (a) the θ-method, (b) the sequential splitting procedure and (c) Richardson Extrapolation. Stability results for the combined numerical method are proved. It is shown, by using numerical experiments, that if the combined numerical method is stable, then it behaves as a second-order method.
Rings of constants of four-variable Lotka-Volterra systems
Lotka-Volterra systems appear in population biology, plasma physics, laser physics and derivation theory, among many others. We determine the rings of constants of four-variable Lotka-Volterra derivations with four parameters C 1, C 2, C 3, C 4 ∈ k, where k is a field of characteristic zero. Thus, we give a full description of polynomial first integrals of the respective systems of differential equations.
Rings of constants of generic 4D Lotka-Volterra systems
We show that the rings of constants of generic four-variable Lotka-Volterra derivations are finitely generated polynomial rings. We explicitly determine these rings, and we give a description of all polynomial first integrals of their corresponding systems of differential equations. Besides, we characterize cofactors of Darboux polynomials of arbitrary four-variable Lotka-Volterra systems. These cofactors are linear forms with coefficients in the set of nonnegative integers. Lotka-Volterra systems...
Rosenbrock Methods for Differential Algebraic Equations.
Roughness of -dichotomies under small perturbations in .