Approximation of eigenvalues of differential equations with non-smooth coefficients
Approximation of Hopf Bifurcation.
Approximation of isolated eigenvalues of ordinary differential operators.
Approximation of limit cycle of differential systems with variable coefficients
The behavior of the approximate solutions of two-dimensional nonlinear differential systems with variable coefficients is considered. Using a property of the approximate solution, so called conditional Ulam stability of a generalized logistic equation, the behavior of the approximate solution of the system is investigated. The obtained result explicitly presents the error between the limit cycle and its approximation. Some examples are presented with numerical simulations.
Approximation of periodic solutions of a system of periodic linear nonhomogeneous differential equations
The present paper does not introduce a new approximation but it modifies a certain known method. This method for obtaining a periodic approximation of a periodic solution of a linear nonhomogeneous differential equation with periodic coefficients and periodic right-hand side is used in technical practice. However, the conditions ensuring the existence of a periodic solution may be violated and therefore the purpose of this paper is to modify the method in order that these conditions remain valid....
Approximation of relaxed solutions for lower semicontinuous differential inclusions
We construct a guided continuous selection for lsc multifunctions with decomposable values in L¹[0,T]. We then apply it to obtain a new result on the uniform approximation of relaxed solutions for lsc differential inclusions.
Approximation of solution of some -point boundary value problems on time scales.
Approximation of solutions of a difference-differential equation
In the present paper we study the approximate solutions of a certain difference-differential equation under the given initial conditions. The well known Gronwall-Bellman integral inequality is used to establish the results. Applications to a Volterra type difference-integral equation are also given.
Approximation of solutions of nonlinear heat transfer problems.
Approximation of solutions of the forced duffing equation with nonlocal discontinuous type integral boundary conditions
A generalized quasilinearization technique is applied to obtain a sequence of approximate solutions converging monotonically and quadratically to the unique solution of the forced Duffing equation with nonlocal discontinuous type integral boundary conditions.
Approximation of solutions to evolution integrodifferential equations.
Approximation of solutions to retarded differential equations with applications to population dynamics.
Approximation of solutions to second order nonlinear Picard problems with Carathéodory right-hand side
We present an approximation method for Picard second order boundary value problems with Carathéodory righthand side. The method is based on the idea of replacing a measurable function in the right-hand side of the problem with its Kantorovich polynomial. We will show that this approximation scheme recovers essential solutions to the original BVP. We also consider the corresponding finite dimensional problem. We suggest a suitable mapping of solutions to finite dimensional problems to piecewise constant...
Approximation of the Solution of a Fourth Order Boundary Value Problem with Nonsmooth Coefficient.
Approximation of the Zakai equation in a nonlinear filtering problem with delay
A nonlinear filtering problem with delays in the state and observation equations is considered. The unnormalized conditional probability density of the filtered diffusion process satisfies the so-called Zakai equation and solves the nonlinear filtering problem. We examine the solution of the Zakai equation using an approximation result. Our theoretical deliberations are illustrated by a numerical example.
Approximation structures and applications to evolution equations.
Approximation theorem for evolution operators
This paper is devoted to the study of the approximation problem for the abstract hyperbolic differential equation u'(t) = A(t)u(t) for t ∈ [0,T], where A(t):t ∈ [0,T] is a family of closed linear operators, without assuming the density of their domains.
Approximation theorems of Wong-Zakai type for stochastic differential equations in infinite dimensions [Book]
Approximation theories for inertial manifolds
Approximation von Eigenwertproblemen bei nichtlinearer Parameterabhängigkeit.