Sentence examples for boundary value problems such from inspiring English sources

This method belongs to the group of methods for solving boundary value problems such as the finite element method (FEM) or the boundary element method (BEM).

Asymptotic boundary value problems such as those governing the boundary layer equations are further complicated by the fact that the outer boundary condition is specified at infinity.

Recently, many researchers pay more attention to the impulsive boundary value problems, such as Dirichlet boundary value problem, periodic boundary value problem, two point boundary value problem and so on (see for example, [9], [10] and references therein).

The model is shown to provide a flexible framework for consistent interpretation of experimental loading paths, and can be readily applied to challenging boundary value problems, such as studying the stability of slopes exposed to acid rain or predicting the effectiveness of CO2 injection in carbonate rocks.

In our earlier work [1, 2] we have shown that the interpolating polynomial theory and the qualitative as well as quantitative study of boundary value problems such as existence and uniqueness of solutions, and convergence of various iterative methods are directly connected.

Although there are several studies about the applications of sinc function-based methods to deterministic boundary value problems such as [12] and [13], the applicability of the sinc functions-based methods has not been investigated in detail at the numerical solutions of fractional order differential equations.

This method works for any boundary value problem such that a uniform anti-maximum principle holds.

Since recently, there are several kinds of boundary conditions in the study of fractional order boundary value problem such as two-point, multi-point, periodic/anti-periodic, nonlocal and integral boundary conditions.

Thus, following the classical techniques introduced by Sattinger [18], we deduce that for a given control (u=lambda u_{1}+ 1-lambda )u_{2}) there exists a solution ψ to the above boundary value problem such that z(x)lepsi(x)le y(x)quadtext{ almost everywhere in $Omega$}.

Therefore, the well-posedness of two-point boundary value problems for such ODEs on arbitrary time duration has very meaningful application background and practical significance.

Let us cite some facts from the theory of functional differential equations [1] and the general description of the constructive approach to the investigation of boundary value problems for such equations [2, 3].