Using classic differential quadrature formulae and uniform grids, this paper systematically constructs a variety of high-order finite difference schemes, and some of these schemes are consistent with the so-called boundary value methods. The derived difference schemes enjoy the same stability and accuracy properties with correspondent differential quadrature methods but have a simpler form of c...

We show there exists a continuous compactly supported function ' de ned on the reals satsifying '(x) = c0'(2x) + c1'(2x 1) + c2'(2x 2) if and only if c1 = 1, c0 + c2 = 1, and jc0j; jc2j < 1. The functions ' are examples of scaling functions from the theory of wavelets. x

Monitoring System has been forthcoming (see March 1996 Colorado Dairy News). Although Colorado was not one of the states sampled. The results on a regional and national basis provide our producers with thoughtprovoking information. The Colorado Dairy News will feature topics from this study in this and future issues. We appreciate the assistance of Dr Scott Wells and his associates at NAHMS wit...

High-order finite difference methods are efficient, easy to program, scale well in multiple dimensions and can be modified locally for various reasons (such as shock treatment for example). The main drawback has been the complicated and sometimes even mysterious stability treatment at boundaries and interfaces required for a stable scheme. The research on summation-byparts operators and weak bo...

and Applied Analysis 3 The grid function y(x, t) is a function defined at the grid points of g. we denote the nodal values of a grid function y(x, t) between time levels t 0 and t 0 as y (x, t) = y (x 1 , x 2 , t l,j i ) = y l,j n1 ,n2 , (11) for x ∈ ω i , i > 0, j = 0, . . . , m i . For x ∈ ω 0 we define y (x, t) = y (x 1 , x 2 , t l+1 0 ) = y l+1 n1 ,n2 . (12) δ x1 , δ x1 and δ x2 , δ x2 are ...

Monotonicity analysis of delta fractional sums and differences order υ∈(0,1] on the time scale hZ are presented in this study. For analysis, two models discrete calculus, Riemann–Liouville Caputo, considered. There is a relationship between h-difference Caputo h-differences, which we find Therefore, after solve one, can apply same method to other one due their correlation. We show that y(z) υ-i...

We review various algorithms for finding apparent horizons in 3+1 numerical relativity. We then focus on one particular algorithm, in which we pose the apparent horizon equation H ≡ ∇in + Kijnn − K = 0 as a nonlinear elliptic (boundary-value) PDE on angular-coordinate space for the horizon shape function r = h(θ, φ), finite difference this PDE, and use Newton’s method or a variant to solve the ...