ALGORITHM 731 - A MOVING-GRID INTERFACE FOR SYSTEMS OF ONE-DIMENSIONAL TIME-DEPENDENT PARTIAL-DIFFERENTIAL EQUATIONS

In the last decade, several numerical techniques have been developed t o solve time-dependent partial differential equations (PDEs) in one di mension having solutions with steep gradients in space and in time. On e of these techniques, a moving-grid method based on a Lagrangian desc ription of the PDE and a smoothed-equidistribution principle to define the grid positions at each time level, has been coupled with a spatia l discretization method that automatically discretizes the spatial par t of the user-defined PDE following the method of lines approach. We s upply two FORTRAN subroutines, CWRESU and CWRESX, which compute the re siduals of the differential algebraic equations (DAE) system obtained from semidiscretizing, respectively, the PDE and the set of moving-gri d equations. These routines are combined in an enveloping routine SKMR ES, which delivers the residuals of the complete DAE system. To solve this stiff, nonlinear DAE system, a robust and efficient time-integrat or must be applied, for example, a BDF method such as implemented in t he DAE solvers SPRINT [Berzins and Furzeland 1985; 1986; Berzins et al . 1989] and DASSL [Brenan et al. 1989; Petzold 1983]. Some numerical e xamples are shown to illustrate the simple and effective use of this s oftware interface.