Mathematical Software (TOMS)


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ACM Transactions on Mathematical Software (TOMS), Volume 17 Issue 2, June 1991

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...