A Collection of Automatic Differentiation Tools 

Automatic differentiation (AD) is a technique for augmenting computer programs with derivative computations. It exploits the fact that every computer program, no matter how complicated, executes a sequence of elementary arithmetic operations such as additions or elementary functions such as exp(). By applying the chain rule of derivative calculus repeatedly to these operations, derivatives of arbitrary order can be computed automatically, and accurate to working precision. The following list of automatic differentiation tools provides a short introduction into the capabilities of the listed AD tool, as provided by their developers and provides pointers to developers and additional information. Submitted: Mar 29, 2000

Software for Initial Value Problems 

The code GAM numerically solves first order ordinary differential equations, either stiff or nonstiff in the form y'=f(x,y), with a given initial condition. The methods used are in the class of Boundary Value Methods (BVMs), namely the Generalized Adams Methods (GAMs) of order 3,5,7,9 with step size control. Submitted: Mar 28, 2000

netlib/ode 

Many ODE solvers. Submitted: Jul 07, 1999

FISHPAK 

This is a free, portable library for the direct solution of finite difference approximations to two dimensional Helmholz equations in Cartesian, polar, cylindrical, interior spherical coordinates, and surface spherical coordinates, with various combinations of periodicity, normal derivative, or solution of the boundaries of a regular domain. Versions of these two dimensional codes are provided for both standard and staggered grids. Additionally, FISHPAK provides two routines for solving more general two dimensional separable elliptic equations, and one routine for solving a system of linear equations resulting from the discretization of a three dimensional separable elliptic equation. Submitted: Mar 27, 2000

BVP Software by Ross Wright and Jeff Cash 

The codes available on this page are for solving boundary value problems for ordinary differential equations. All of the codes are included under the ode directory of netlib and are written in FORTRAN 77 and use double precision arithmetic. All compressed files are created by using the command "gzip" (simply "gunzip" them at your end). Submitted: Jul 07, 1999

DVERK 

A public domain Fortran 77 subroutine written by Hull, Enright and Jackson for the numerical solution of systems of initial value problems for ordinary differential equations. Submitted: Mar 01, 2000

ODE Software by Jeff Cash 

This describes the codes and results which allow the comparison of MEBDF.f ,Radau5.f , sprint.f and lsode.f on various test problems. The code mebdf.f is being updated to allow the solution of daes and it is hoped to release this new code in the near future. Submitted: Jul 07, 1999

IVP Software by Jeff Cash 

The code MEBDFDAE is designed to solve stiff initial value problems and differential algebraic equations. MEBDF is described in Hairer and Wanner [1]. Submitted: Jul 07, 1999

