The software package PDECOL [7] is a popular code among scientists wishing to solve systems of nonlinear partial differential equations. The code is based on a method-of-lines approach, with collocation in the space variable to reduce the problem to a system of ordinary differential equations. There are three principal components: the basis functions employed in the collocation; the method used to solve the system of ordinary differential equations; and the linear equation solver which handles the linear algebra. This paper will concentrate on the third component, and will report on the improvement in the performance of PDECOL resulting from replacing the current linear algebra modules of the code by modules which take full advantage of the special structure of the equations which arise. Savings of over 50 percent in total execution time can be realized. (Source: http://dl.acm.org/)

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 14 articles , 1 standard article )

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  1. Muir, Paul; Pew, Jack: An analysis of the reliability of error control B-spline Gaussian collocation PDE software (2016)
  2. Wang, Qiming: Stability and breakup of liquid threads and annular layers in a corrugated tube with zero base flow (2016)
  3. El-Mistikawy, Tarek M.A.: Modular analysis of sequential solution methods for almost block diagonal systems of equations (2013)
  4. Sileri, D.; Sahu, K.C.; Matar, O.K.: Two-fluid pressure-driven channel flow with wall deposition and ageing effects (2011)
  5. 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)
  6. Matar, Omar K.; Kumar, Satish: Dynamics and stability of flow down a flexible incline (2007)
  7. Wang, R.; Keast, P.; Muir, P.: A high-order global spatially adaptive collocation method for 1-D parabolic PDEs (2004)
  8. Wang, R.; Keast, P.; Muir, P.: BACOL: B-spline adaptive collocation software for 1-D parabolic PDEs (2004)
  9. Wang, Rong; Keast, Patrick; Muir, Paul: A comparison of adaptive software for 1D parabolic PDEs (2004)
  10. Bialecki, B.; Fairweather, G.: Orthogonal spline collocation methods for partial differential equations (2001)
  11. Moore, Peter K.: Comparison of adaptive methods for one-dimensional parabolic systems (1995)
  12. Carroll, John: A composite integration scheme for the numerical solution of systems of parabolic PDEs in one space dimension (1993)
  13. Berzins, M.; Dew, P.M.: Algorithm 690: Chebyshev polynomial software for elliptic-parabolic systems of PDEs (1991)
  14. Keast, P.; Muir, P.H.: Algorithm 688: EPDCOL: A more efficient PDECOL code (1991)