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ACM Transactions on Mathematical Software (TOMS), Volume 28 Issue 1, March 2002

Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL
K. Engelborghs, T. Luzyanina, D. Roose
Pages: 1-21
DOI: 10.1145/513001.513002
We describe DDE-BIFTOOL, a Matlab package for numerical bifurcation analysis of systems of delay differential equations with several fixed, discrete delays. The package implements continuation of steady state solutions and periodic solutions and...

Efficient and automatic implementation of the adjoint state method
Mark S. Gockenbach, Daniel R. Reynolds, Peng Shen, William W. Symes
Pages: 22-44
DOI: 10.1145/513001.513003
Combination of object-oriented programming with automatic differentiation techniques facilitates the solution of data fitting, control, and design problems driven by explicit time stepping schemes for initial-boundary value problems. The C++ class...

An extension of the divide-and-conquer method for a class of symmetric block-tridiagonal eigenproblems
Wilfried N. Gansterer, Robert C. Ward, Richard P. Muller
Pages: 45-58
DOI: 10.1145/513001.513004
A divide-and-conquer method for computing eigenvalues and eigenvectors of a block-tridiagonal matrix with rank-one off-diagonal blocks is presented. The implications of unbalanced merging operations due to unequal block sizes are analyzed and...

Renovating the collected algorithms from ACM
Tim Hopkins
Pages: 59-74
DOI: 10.1145/513001.513005
Since 1960 the Association for Computing Machinery has published a series of refereed algorithm implementations known as the Collected Algorithms of the ACM (CALGO). Most of those published since 1975 are mathematical algorithms, and many of them...

Algorithm 816: r2d2lri: an algorithm for automatic two-dimensional cubature
Ian Robinson, Michael Hill
Pages: 75-100
DOI: 10.1145/513001.513006
r2d2lri is a non-adaptive algorithm implemented in C++ for performing automatic cubature over a wide variety of finite and non-finite two-dimensional domains. The core integrator uses a sixth-order Sidi transformation applied to a sequence of...

Algorithm 817: P2MESH: generic object-oriented interface between 2-D unstructured meshes and FEM/FVM-based PDE solvers
Enrico Bertolazzi, Gianmarco Manzini
Pages: 101-132
DOI: 10.1145/513001.513007
The software interface P2MESH is a collection of C++ class templates suitable for developing prototypes of high-performance PDE solvers on unstructured 2-D meshes. P2MESH supports several discretization methods on triangles and quadrilaterals, such...