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By Bott, T.F.; Eisenhawer, S.W.; Los Alamos National Laboratory.; United States. Dept. of Energy.; United States. Dept. of Energy. Office of Scientific and Technical Information

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Extra resources for A hazards analysis of a nuclear explosives dismantlement

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Several Examples of H B - Q F In this section, quadrature formulas of general Hermite and Euler-Maclaurin-like types are illustrated together with the Euler-Maclaurin quadrature formula as typical examples of HB-QF. In particular a feature of the Euler-Maclaurin-like type quadrature is to use even order derivatives in the formula, though the Euler-Maclaurin quadrature uses odd order derivatives. 4-3- Quadrature Formula of General Hermite Type Let ni and n (n. < 112) be non-negative integers and n = n.

Hence we have a collocation RK formula. From the derivation of HIDM, it is obvious that the equidistant points = a + (jjm)H stand for the interpolating points with the step-size H. This implies that the formula is the Newton- Cotes type mentioned in Section 2, and that the formula parameter is uniquely determined. It also assures the nonsingularity of the matrix V. jp ABSTRACT A certain type of P-stabJe block method is derived for solving second order initial value problem y" — f(x,y). The block method considered here computes the numerical solutions simultaneously at the two points of x, and is easily paralletisable.

W , / a 0 VJ 56 at 2 = 1. Therefore by the principle of the maximum in the complex-valued function, it follows that S(z) < 1 for any zsC (Rez > 0). We have completed the proof of Theorem 6. It should be noted that the scheme (18) with m = 0 and n = n is equivalent to the Taylor expansion method. 2. Application to Higher Order Ordinary Differential Equation We construct a numerical integration scheme for solving an initial value problem of the r-th order ordinary differential equation given in Eq.

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