Abstract: ODEPACK solves for the initial value problem for ordinary differential equation systems. It consists of nine solvers, a basic solver called LSODE and eight variants of it: LSODES, LSODA, LSODAR, LSODPK, LSODKR, LSODI, LSOIBT, and LSODIS. The collection is suitable for both stiff and nonstiff systems. It includes solvers for systems given in explicit form, dy/dt = f(t,y), and also solvers for systems given in linearly implicit form, A(t,y) dy/dt = g(t,y). The ODEPACK solvers are written in standard Fortran and there are separate double and single precision versions. Each solver consists of a main driver subroutine having the same name as the solver and some number of subordinate routines. For each solver, there is also a demonstration program, which solves one or two simple problems in a somewhat self-checking manner.
Credit: Hindmarsh, Alan C.