CWRESU
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 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.
This software is also peer reviewed by journal TOMS.
This software is also peer reviewed by journal TOMS.
Keywords for this software
References in zbMATH (referenced in 37 articles , 1 standard article )
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- Saucez, P.; Some, L.; Vande Wouwer, A.: Matlab implementation of a moving grid method based on the equidistribution principle (2009)
- Wang, R.; Keast, P.; Muir, P. H.: Algorithm 874: BACOLR -- spatial and temporal error control software for PDEs based on high-order adaptive collocation. (2008)
- Beck, M.; Doelman, A.; Kaper, T. J.: A geometric construction of traveling waves in a bioremediation model (2006)
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- Cheng, H.; Lin, P.; Sheng, Q.; Tan, R. C. E.: Solving degenerate reaction-diffusion equations via variable step Peaceman-Rachford splitting (2003)
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