Distribution of mathematical software via electronic mail
Communications of the ACM
Simple adaptive grids for 1-d initial value problems
Journal of Computational Physics
Algorithm 665: Machar: a subroutine to dynamically determined machine parameters
ACM Transactions on Mathematical Software (TOMS)
Applied Numerical Mathematics
A method for the spatial discretization of parabolic equations in one space variable
SIAM Journal on Scientific and Statistical Computing
Software for Nonlinear Partial Differential Equations
ACM Transactions on Mathematical Software (TOMS)
A moving mesh method for the solution of the one-dimensional phase-field equations
Journal of Computational Physics
A high-order global spatially adaptive collocation method for 1-D parabolic PDEs
Applied Numerical Mathematics
A comparison of adaptive software for 1D parabolic PDEs
Journal of Computational and Applied Mathematics
BACOL: B-spline adaptive collocation software for 1-D parabolic PDEs
ACM Transactions on Mathematical Software (TOMS)
A MATLAB implementation of upwind finite differences and adaptive grids in the method of lines
Journal of Computational and Applied Mathematics - Special issue on the method of lines: Dedicated to Keith Miller
A simple moving mesh method for one-and two-dimensional phase-field equations
Journal of Computational and Applied Mathematics - Special issue: International conference on mathematics and its application
ACM Transactions on Mathematical Software (TOMS)
A MATLAB implementation of upwind finite differences and adaptive grids in the method of lines
Journal of Computational and Applied Mathematics - Special issue on the method of lines: Dedicated to Keith Miller
A simple moving mesh method for one- and two-dimensional phase-field equations
Journal of Computational and Applied Mathematics
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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.