GEARS: a package for the solution of sparse, stiff ordinary differential equations. [In Fortran]

TL;DRAbstract

This paper describes GEARS, a package of Fortran subroutines designed to solve stiff systems of ordinary differential equations of the form dy/dt = f(y,t), where the Jacobian matrices J = par. delta f/par. delta y are large and sparse. The integrator is based on the stiffly stable methods due to Gear, and this approach leads to a sparse system of nonlinear equations at each time step. These are solved with a modified Newton iteration, using one of two separate sparse matrix packages to solve the sparse linear equations that arise. This paper describes the package, in some detail, discusses a number of issues that affected the design of the package, and presents a numerical example to illustrate the effectiveness of the package. 1 figure, 1 table.

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