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.

References in zbMATH (referenced in 37 articles , 1 standard article )

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  1. Craster, R. V.; Matar, O. K.; Papageorgiou, D. T.: Pinchoff and satellite formation in surfactant covered viscous threads (2002)
  2. Mackenzie, J. A.; Robertson, M. L.: A moving mesh method for the solution of the one-dimensional phase-field equations (2002)
  3. Matar, O. K.: Nonlinear evolution of thin free viscous films in the presence of soluble surfactant (2002)
  4. Matar, O. K.; Craster, R. V.; Warner, M. R. E.: Surfactant transport on highly viscous surface films (2002)
  5. Warner, M. R. E.; Craster, R. V.; Matar, O. K.: Unstable Van der waals driven line rupture in marangoni driven thin viscous films (2002)
  6. Hek, Geertje: Fronts and pulses in a class of reaction-diffusion equations: A geometric singular perturbation approach (2001)
  7. Balmforth, N. J.; Burbidge, A. S.; Craster, R. V.; Salzig, J.; Shen, A.: Visco-plastic models of isothermal lava domes (2000)
  8. Champneys, A. R.; McKenna, P. J.; Zegeling, P. A.: Solitary waves in nonlinear beam equations: Stability, fission and fusion (2000)
  9. Morgan, David S.; Doelman, Arjen; Kaper, Tasso J.: Stationary periodic patterns in the 1D Gray-Scott model (2000)
  10. Balmforth, N. J.; Craster, R. V.; Malham, S. J. A.: Unsteady fronts in an autocatalytic system (1999)
  11. Doelman, Arjen; Gardner, Robert A.; Kaper, Tasso J.: Stability analysis of singular patterns in the 1D Gray-Scott model: a matched asymptotics approach (1998)
  12. Rottschäfer, Vivi; Doelman, Arjen: On the transition from the Ginzburg-Landau equation to the extended Fisher-Kolmogorov equation (1998)
  13. Saucez, P.; Vande Wouwer, A.; Schiesser, W. E.: An adaptive method of lines solution of the Korteweg-de Vries equation (1998)
  14. Vande Wouwer, A.; Saucez, P.; Schiesser, W. E.: Some user-oriented comparisons of adaptive grid methods for partial differential equations in one space dimension (1998)
  15. Doelman, Arjen; Kaper, Tasso J.; Zegeling, Paul A.: Pattern formation in the one-dimensional Gray-Scott model (1997)
  16. Moore, Peter K.; Dillon, Robert H.: A comparison of preconditioners in the solution of parabolic systems in three space dimensions using DASPK and a high order finite element method (1996)
  17. Blom, J. G.; Zegeling, P. A.: Algorithm 731: A moving-grid interface for systems of one-dimensional time-dependent partial differential equations (1994)