**Algorithm 786: multiple-precision complex arithmetic and functions**

David M. Smith

Pages: 359-367

DOI: 10.1145/293686.293687

This article describes a collection of Fortran routines for multiple-precision complex arithmetic and elementary functions. The package provides good exception handling, flexible input and output, trace features, and results that are almost...

**Stiffness detection and estimation of dominant spectrum with explicit Runge-Kutta methods**

Kersti Ekeland, Brynjulf Owren, Eivor Øines

Pages: 368-382

DOI: 10.1145/293686.287641

A new stiffness detection scheme based on explicit Runge-Kutta methods is proposed. It uses a Krylov subspace approximation to estimate the eigenvalues of the Jacobian of the differential system. The numerical examples indicate that this...

**Remark on algorithm 761**

Robert J. Renka, Ron Brown

Pages: 383-385

DOI: 10.1145/293686.293689

Several inprovements to algorithm 761 are presented. The problems corrected consist of (1) the computation of a determinant in subroutine SDLEQN may result in overflow, (2) subroutine SDTRCH may fail to correctly determine the set of boundary...

**Algorithm 787: Fortran subroutines for approximate solution of maximum independent set problems using GRASP**

Mauricio G. C. Resende, Thomas A. Feo, Stuart H. Smith

Pages: 386-394

DOI: 10.1145/293686.293690

Let G=(V, E) be an undirected graph where V and E are the sets of vertices and edges of G, respectively. A subset of the vertices S
⊆ V is independent if all of its members are pairwise...

**Algorithm 788: automatic boundary integral equation programs for the planar Laplace equation**

Kendall Atkinson, Youngmok Jeon

Pages: 395-417

DOI: 10.1145/293686.293692

Algorithms with automatic error control are described for the solution of Laplace's equation on both interior and exterior regions, with both Dirichlet and Neumann boundary conditions. The algorithms are based on standard reformulations of each...

**Implementation of Hopf and double-Hopf continuation using bordering methods**

W. Govaerts, Yu. A. Kuznetsov, B. Sijnave

Pages: 418-436

DOI: 10.1145/293686.293693

We discuss the computational study of curves of Hopf and double-Hopf points in the software package CONTENT developed at CWI, Amsterdam. These are important points in the numerical study of dynamical systems characterized by the occurrence of...

**Recipes for adjoint code construction**

Ralf Giering, Thomas Kaminski

Pages: 437-474

DOI: 10.1145/293686.293695

Adjoint models are increasingly being developed for use in meteorology and oceanography. Typical applications are data assimilation, model tuning, sensitivity analysis, and determination of singular vectors. The adjoint model computes the...

**SPRINT2D**: adaptive software for PDEs

M. Berzins, R. Fairlie, S. V. Pennington, J. M. Ware, L. E. Scales

Pages: 475-499

DOI: 10.1145/293686.293696

SPRINT2D is a set of software tools for solving both steady an unsteady partial differential equations in two-space variables. The software consists of a set of coupled modules for mesh generation, spatial discretization, time integration,...