Name
Title | ||
|---|---|---|
Algorithm 731: A moving-grid interface for systems of one-dimensional time-dependent partial differential equations |
Abstract | ||
|---|---|---|
In the last decade, several numerical techniques have been developed to solve time-dependent partial differential equations (PDEs) in one dimension having solutions with steep gradients in space and in time. One of these techniques, a moving-grid method based on a Lagrangian description of the PDE and a smoothed-equidistribution principle to define the grid positions at each time level, has been coupled with a spatial discretization method that automatically discreizes the spatial part of the user-defined PDE following the method of lines approach. We supply two FORTRAN subroutines, CWRESU and CWRESX, which compute the residuals of the differential algebraic equations (DAE) system obtained from semidiscretizing, respectively, the PDE and the set of moving-grid equations. These routines are combined in an enveloping routine SKMRES, which delivers the residuals of the complete DAE system. To solve this stiff, nonlinear DAE system, a robust and efficient time-integrator must be applied, for example, a BDF method such as implemented in the DAE solvers SPRINT [Berzins and Furzeland 1985; 1986; Berzins et al. 1989] and DASSL [Brenan et al. 1989; Petzold 1983]. Some numerical examples are shown to illustrate the simple and effective use of this software interface. |
Year | DOI | Venue |
|---|---|---|
1994 | 10.1145/178365.178391 | ACM Trans. Math. Softw. |
Keywords | Field | DocType |
moving grids,mathematical software,lagrangian methods,nonlinear dae system,moving-grid equation,partial differential equations,differential algebraic equation,moving-grid method,spatial discretization method,complete dae system,dae solvers sprint,moving-grid interface,bdf method,user-defined pde,numerical example,time-dependent problems,method of lines,one-dimensional time-dependent partial differential,partial differential equation | Discretization,Mathematical optimization,Nonlinear system,Mathematical analysis,Algorithm,Fortran,Differential algebraic equation,Method of lines,Mathematical software,Partial differential equation,Grid,Mathematics | Journal |
Volume | Issue | ISSN |
20 | 2 | 0098-3500 |
Citations | PageRank | References |
9 | 1.78 | 4 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Joke G Blom | 1 | 161 | 23.43 |
| P. A. Zegeling | 2 | 25 | 6.15 |