It is well known that the problem of estimating the state and parameters of discrete-time nonlinear dynamic systems from noisy measurements can be formulated as a nonlinear two-point boundaryvalue problem. In this paper, an algorithm is developed for solving the above boundary-value problem. The algorithm, which is based on Newton's method, requires very little storage. A detailed discussion of...

In this article, we are concerned with the existence, uniqueness and asymptotic behavior of a positive classical solution to the semilinear boundaryvalue problem −∆u = a(x)u in D, lim |x|→1 u(x) = lim |x|→∞ u(x) = 0. Here D is the complement of the closed unit ball of Rn (n ≥ 3), σ < 1 and the function a is a nonnegative function in C loc(D), 0 < γ < 1, satisfying some appropriate assumptions r...

Directional emission from a slit surrounded by rectangular grooves on the exit surface in a conducting plane is investigated. An electromagnetic boundaryvalue problem dealing with a slit surrounded by rectangular grooves on the exit surface in a conducting plane is rigourously solved based on the Fourier transform, eigenfunction expansion, and mode-matching method. The radiation pattern from th...

We obtain sufficient conditions, easily verifiable, for the existence and uniqueness of piecewise smooth solutions of a linear two-point boundaryvalue problem with general interface conditions. The coefficients of the differential equation may have jump discontinuities at the interface point. As an example, the conditions obtained are applied to a problem with typical interface such as perfect ...

We describe a robust correction to Black-Scholes American derivatives prices that accounts for uncertain and changing market volatility. It exploits the tendency of volatility to cluster, or fast mean-reversion, and is simply calibrated from the observed implied volatility skew. The two-dimensional free-boundary problem for the derivative pricing function under a stochastic volatility model is ...

Calculation schemes for numerical solution of elliptic boundary-value problems for Schrödinger-type equations based on Kantorovich method that reduces the initial problem to a set of boundary-value problems for a system of ordinary second-order differential equations are presented. The reduced boundaryvalue problems are discretized using the high-accuracy finite element method and implemented i...

Free high-frequency longitudinal vibrations of an inhomogeneous nanosized rod are studied on the basis nonlocal theory elasticity. The upper part spectrum with wavelength comparable to internal characteristic dimension a nanorod is examined. An equations in integral form Helmholtz kernel, incorporating both local and phases, used as constitutive one. original integro-differential equation reduc...

In this article, we study a class of nonlinear singular boundaryvalue problems. We show the existence of positive weak solutions by using variational methods.

In this paper, we present necessary and sufficient conditions for the existence of positive C3[0, 1]∩C4(0, 1) solutions for the singular boundaryvalue problem x′′′′(t) = p(t)f(x(t)), t ∈ (0, 1); x(0) = x(1) = x′(0) = x′(1) = 0, where f(x) is either superlinear or sublinear, p : (0, 1) → [0,+∞) may be singular at both ends t = 0 and t = 1. For this goal, we use fixed-point index results.

In this paper, a spline finite element approach is manipulated for the numerical solution of an extended system of second-order boundaryvalue problems. The efficiency of the proposed method is examined by comparing the results with the existing exact closed form solution. The numerical results demonstrate that the method is efficient and quite accurate when contrasted with other methods and req...