**Algorithm 688: EPDCOL**: a more efficient PDECOL code

P. Keast, P. H. Muir

Pages: 153-166

DOI: 10.1145/108556.108558

The software package PDECOL [7] is a popular code among scientists wishing to solve systems of nonlinear partial differential equations. The code is based on a method-of-lines approach, with collocation in the space variable to reduce the...

**Algorithm 689: Discretized collocation and iterated collocation for nonlinear Volterra integral equations of the second kind**

J. G. Blom, H. Brunner

Pages: 167-177

DOI: 10.1145/108556.108562

This paper describes a FORTRAN code for calculating approximate solutions to systems of nonlinear Volterra integral equations of the second kind. The algorithm is based on polynomial spline collocation, with the possibility of combination with...

**Algorithm 690: Chebyshev polynomial software for elliptic-parabolic systems of PDEs**

M. Berzins, P. M. Dew

Pages: 178-206

DOI: 10.1145/108556.108566

PDECHEB is a FORTRAN 77 software package that semidiscretizes a wide range of time-dependent partial differential equations in one space variable. The software implements a family of spacial discretization formulas, based on piecewise Chebyshev...

**Interpolatory integration formulas for optimal composition**

Paola Favati, Grazia Lotti, Francesco Romani

Pages: 207-217

DOI: 10.1145/108556.108571

A set of symmetric, closed, interpolatory integration formulas on the interval [-1, 1] with positive weights and increasing degree of precision is introduced. These formulas, called recursive monotone stable (RMS) formulas, allow applying higher...

**Algorithm 691: Improving QUADPACK automatic integration routines**

Paola Favati, Grazia Lotti, Francesco Romani

Pages: 218-232

DOI: 10.1145/108556.108580

Two automatic adaptive integrators from QUADPACK (namely, QAG, and QAGS) are modified by substituting the Gauss-Kronrod rules used for local quadrature with recursive monotone stable (RMS) formulas. Extensive numerical tests, both for...

**Error estimation in automatic quadrature routines**

Jarle Berntsen, Terje O. Espelid

Pages: 233-252

DOI: 10.1145/108556.108575

A new algorithm for estimating the error in quadrature approximations is presented. Based on the same integrand evaluations that we need for approximating the integral, one may, for many quadrature rules, compute a sequence of null rule...

**Sparse extensions to the FORTRAN Basic Linear Algebra Subprograms**

David S. Dodson, Roger G. Grimes, John G. Lewis

Pages: 253-263

DOI: 10.1145/108556.108577

This paper describes an extension to the set of Basic Linear Algebra Subprograms. The extension is targeted at sparse vector operations, with the goal of providing efficient, but portable, implementations of algorithms for high-performance...

**Algorithm 692: Model implementation and test package for the Sparse Basic Linear Algebra Subprograms**

David S. Dodson, Roger G. Grimes, John G. Lewis

Pages: 264-272

DOI: 10.1145/108556.108582

This paper desribes a model implementation and test software for the Sparse Basic Linear Algebra Subprograms (Sparse BLAS). The Sparse BLAS perform vector operations common in sparse linear algebra, with the goal of providing efficient, but...

**Algorithm 693: a FORTRAN package for floating-point multiple-precision arithmetic**

David M. Smith

Pages: 273-283

DOI: 10.1145/108556.108585

FM is a collection of FORTRAN-77 routines which performs floating-point multiple-precision arithmetic and elementary functions. Results are almost always correctly rounded, and due to improved algorithms used for elementary functions, reasonable...