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 .
Second derivative linear multistep formula and its stability on the imaginary axis
Second Order Nonlinear Differential Equations Equivalent To Linear Differential Equations
Second order nonlinear differential equations equivalent to linear differential equations.
Simulation of analog computer in solving non-linear differential equations by a digital computer
Singular solutions of a singular differential equation.
Smooth factorizations of matrix valued functions and their derivatives.
Solution of an extraordinary differential equation by Adomian decomposition method.
Solutions of nonhomogeneous linear differential equations with exceptionally few zeros.
Solutions to Lyapunov stability problems: Nonlinear systems with continuous motions.
Solutions to Lyapunov stability problems of sets: Nonlinear systems with differentiable motions.
Solvability of an Infinite System of Singular Integral Equations
2000 Mathematics Subject Classification: 45G15, 26A33, 32A55, 46E15.Schauder's fixed point theorem is used to establish an existence result for an infinite system of singular integral equations in the form: (1) xi(t) = ai(t)+ ∫t0 (t − s)− α (s, x1(s), x2(s), …) ds, where i = 1,2,…, α ∈ (0,1) and t ∈ I = [0,T]. The result obtained is applied to show the solvability of an infinite system of differential equation of fractional orders.
Solvability of nonlinear Langevin equation involving two fractional orders with Dirichlet boundary conditions.
Solving dynamical systems with cubic trigonometric splines.