Because of these reasons,putting forward Runge phenomenon,designing a principal-agent range model. On base of this model,to make consignor and agent aim same,to increase corporate value,put forward two ways of reducing contract effective angle,including executive stock options and construction of independent director.

But with the increasing of the order of interpolation polynomials, serious oscillation phenomena will appear, which will increase the computational error and affect instabilities of computations.

Introduced in the higher-order interpolation the Runger phenomenon production,and on the Newton interpolation, comes using the computer program,the test appears of the Runger phenomenon,has produced the corresponding algorithm realization.

But with the increasing of the order of interpolation polynomials, serious oscillation phenomena will appear, which will increase the computational error and affect instabilities of computations.

No filtering is done; with ten coarse grid points in the front, the Runge phenomenon was not observed.

This so-called Runge phenomenon is not a problem with the barycentric formula, but is intrinsic in the underlying interpolation problem.

Thus, an important issue in high-order AMR is dealing with the potential for the Runge phenomenon associated with interpolation on uniform grids.

In the present paper the convergence and validity of the results of boundary collocation procedure are studied by considering function approxima- tion. The problem being discussed here is one of rectangular plates with one- side edge crack, and the Williams stress function is used as approximating function. For examining the validity of the results a criterion, based on considering uniform approximation of functions, is put forward. Suppose that in the problem the boundary condition is known as f(s) (where...

In the present paper the convergence and validity of the results of boundary collocation procedure are studied by considering function approxima- tion. The problem being discussed here is one of rectangular plates with one- side edge crack, and the Williams stress function is used as approximating function. For examining the validity of the results a criterion, based on considering uniform approximation of functions, is put forward. Suppose that in the problem the boundary condition is known as f(s) (where s represents points on the boundary B), which-is approximated by the Williams stress function W_m (s). Now if the solution of the boundary value problem is stable, then a small difference between W_m (s) and f(s) would cause only a small deviation ω(γ,θ) of the calculated solution from the exact solution, where γ, θ are polar coordinates of points in domain D bounded by boundary B. Hence the mag- nitude of |δ(s)|_(max) represents a measure of the quality of the solution in domain D. For the convenience of calculation, |δ(s)|_(max) is replaced by the relative mean square error M_δ, as "criterion of validity". The criterion can be given as M_δ=(∫_B δ~2 (s)ds)/(∫_B f~2 (s)ds ≤ε where ε is a small value depending upon the accuracy required in the calcula- tion. With the help of this criterion, a judgement about the validity of the results can be obtained from the calculation itself, without having to rely on previously known analytic solution. The effectiveness of the criterion put forward is proved in numerical examples given in this paper. The difference in convergence of two different approximations usually used, i, e., interpolation approximation and average approximation, is discussed. It is well known that the results of interpolation approximation are not always convergent. This is usually explained as follows: "As in the coefficient matrix the differences between two adjacent columns are very small, the results become unstable". That is to say, divergence occurs because of the errors in matrix calculation. However, it is found in our calculations that the errors of the approximating function W_m(s) at all the nodes are negligibly small (δ(s)→0 at nodes). This clearly shows that the errors in matrix calculation appear to be not the real reason of the divergence. It is shown in the present paper that, at least for the problem studied, the divergence results from the the fluctuation of the approximating function between the nodes, and that the situation becomes worse as the number of nodes increases. This is known as "Runge phenomenon" in algebraic interpo- lation. For average approximation, there will be no fluctuation in general, and the solutions can be shown to be always convergent, but it may or may not converge to the exact solution of the problem This seems to be an indication of the incompleteness of the Williams function.

Due to long span and diverse shape of long-span roofs, airflow will separate and re-attach and then wind pressure distribution will be complicated. Rigid model wind tunnel test is a useful method to obtain wind pressure coefficients on the limited measuring point. In this paper, piecewise low-order interpolation method of two-dimensional and multi-dimensional function is used to determine wind pressure distributions on the whole roof surface. This method can avoid "Runge" phenomenon of high-order interpolation....

Due to long span and diverse shape of long-span roofs, airflow will separate and re-attach and then wind pressure distribution will be complicated. Rigid model wind tunnel test is a useful method to obtain wind pressure coefficients on the limited measuring point. In this paper, piecewise low-order interpolation method of two-dimensional and multi-dimensional function is used to determine wind pressure distributions on the whole roof surface. This method can avoid "Runge" phenomenon of high-order interpolation. Edge region and irregular plane shape can be dealt with by extrapolation. Wind pressure distributions on spherical shell or curving roofs can be obtained by the method of coordinate transform or projected plane of curved surface.

Introduced in the higher-order interpolation the Runger phenomenon production,and on the Newton interpolation, comes using the computer program,the test appears of the Runger phenomenon,has produced the corresponding algorithm realization.