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- George D. Byrne, Alan C. Hindmarsh
- ACM Trans. Math. Softw.
- 1975

Two variable-order, varlable-step size methods for the numerical solution of the initial value problem for ordinary differential equations are presented. These methods share a common philosophy and have been combined in a single program. The two integrators are for stiff and nonstiff ordinary differential equations, respectively. The former integrator is… (More)

- N. M. Steen, G. D. Byrne, E. M. Gelbard, E. M. GELBAKD
- 2010

Gaussian quadratures are developed for the evaluation of the integrals given in the title. The weights and abscissae for the semi-infinite integral are given for two through fifteen points with fifteen places. For 6 = 1, the weights and abscissae are given for two through ten points with fifteen places. 1. Introduction. In nuclear reactor design… (More)

- George D. Byrne, Robert J. Lambert
- J. ACM
- 1966

A third order two step method and a fourth order two step method for the numerical solution of the vector initial value problem <italic>dy</italic> ÷ <italic>dx</italic>=F(y), y(<italic>a</italic>) = n can be defined by making evaluations of F similar to those found in a classical Runge-Kutta formula. These two step methods are different from classical… (More)

- George D. Byrne, Alan C. Hindmarsh
- IJHPCA
- 1999

- L L Reti, G D Byrne, R A Davoren
- The Australian & New Zealand journal of…
- 1983

The acute effects of retrograde menstruation were studied by endoscopy and cytology. The findings suggest that spillage of menstrual blood into the peritoneal cavity is painful. The technique of making this diagnosis is discussed and the therapeutic implications considered.

- George D. Byrne, Anthony M. Dean
- Computers & Chemistry
- 1993

- George D. Byrne
- Commun. ACM
- 1967

If u and P are 2V-dhuensiomfl vectors a:ud cx, ~, % (3 are matrices of order N, the atmlogue of eq, (:12) is dA'/dT = ~ + c~,9 + Ra + lgvtf, as shown i~ [6]. The correspondiug equatiol~ for ,u(t) = Z(7'~c is 2 *:) Qe~) dZ, It. has been shown in several ex:m~ples that, iu some cases, one can convert unstable boundary-value problems into stable initial-value… (More)

- George D. Andria, George D. Byrne, David R. Hill, GEORGE D. ANDRIA, GEORGE D. BRYNE
- 2010

Numerical integration formulas of interpolatory type are generated by the integration of g-splines. These formulas, which are best in the sense of Sard, are used to construct predictor-corrector and block implicit schemes. The schemes are then compared with Adams-Bashforth-Adams-Moulton and Rosser schemes for a particular set of prototype problems.… (More)

- George D. Byrne
- IMPACT Comput. Sci. Eng.
- 1993

- A. C. Hindmarsh, G. D. Byrne
- SGNM
- 1976

The idea of rank-one updates for the inverse of the Newton iteration matrix is considered in the context of solving stiff systems of ordinary differential equations. A specific and simple problem (linear, with a constant, diagonal Jacobian) and a specific and simple method (backward Euler, with constant step) are studied. A Newton iteration matrix which is… (More)