# George D. Byrne

• 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)
• 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> &#247; <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)
• IJHPCA
• 1999
PVODE is a generalpurpose solver for or di nary dif fer en tial equa tion (ODE) sys tems that im ple ments meth ods for both stiff and non stiff sys tems. The code is de signed for singleprogram multipledata en vi ron ments. It is writ ten in ANSI stan dard C, with a highly modu lar struc ture. The ver sion be ing dis trib uted uses the messagepassing in(More)
• 1
• 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)
• 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)
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