Good Initial Value Research Articles

Large ordinary differential equation systems and software

Over the last decade, the need to solve large stiff and nonstiff ordinary differential equation systems (initial value problems) has led to considerable software, mostly based on the methods of Adams (nonstiff case) and Gear (stiff case). The growing number of good general purpose initial value solvers has fueled discussions on the idea of a systematized collection of such solvers, called ODE-PACK. In recent years, a tentative user interface standard was developed, and an initial collection of five solvers was written, primarily at LLNL. These solvers handle stiff and nonstiff problems posed in standard (explicit) form, problems in linearly implicit form, full Jacobians, banded Jacobians, general sparse Jacobians, and problems with rootfinding requirements. They include solvers with automatic (stiff/nonstiff) method selection. These solvers are described briefly here, and their capabilities are illustrated with an example problem arising from a system of PDE's modeling atmospheric kinetics-transport.

2段階線形計画問題に対する2-レベル分割解法

An algorithm for solving 2-stage linear programs. especially useful for 11 program arising from a nested multi·level approach to multi-period planning (3) is presented. The proposed algorithm is of a two·level scheme and similar to Beale's method (4), but the procedure is more systematic and simpler. Computational experience is reported for a series of small test problems. The results show that our algorithm is more efficient than a Beale-Iike method. and moreover that the number of times for adjusting given initial values of linking variables is unexpectedly small for the test problems, which may also imply an aspect of usefulness of the algorithm for large real problems, especially when a good initial value can be obtained for the linking variable. The algorithm can be also extended to a weakly coupled three or more-stage case.