Volume 5, Issue 4
B-Spline Gaussian Collocation Software for Two-Dimensional Parabolic PDEs

Zhi Li & Paul Muir

Adv. Appl. Math. Mech., 5 (2013), pp. 528-547.

Published online: 2013-08

Preview Full PDF 2 581
Export citation
  • Abstract

In this paper we describe new B-spline Gaussian collocation software for solving two-dimensional parabolic partial differential equations (PDEs) defined over a rectangular region. The numerical solution is represented as a bi-variate piecewise polynomial (using a tensor product B-spline basis) with  time-dependent unknown coefficients. These coefficients are determined by imposing collocation conditions: the numerical solution is required to satisfy the PDE and boundary conditions at images of the Gauss points mapped onto certain subregions of the spatial domain. This leads to a large system of time-dependent differential algebraic equations (DAEs) which is solved using the DAE solver, DASPK. We provide numerical results in which we use the new software, called BACOL2D, to solve three test problems.

  • Keywords

Collocation B-splines two-dimensional partial differential equations differential-algebraic equations

  • AMS Subject Headings

65M20 65M70

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • References
  • Hide All
    View All

@Article{AAMM-5-528, author = {Zhi Li and Paul Muir}, title = {B-Spline Gaussian Collocation Software for Two-Dimensional Parabolic PDEs}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2013}, volume = {5}, number = {4}, pages = {528--547}, abstract = {

In this paper we describe new B-spline Gaussian collocation software for solving two-dimensional parabolic partial differential equations (PDEs) defined over a rectangular region. The numerical solution is represented as a bi-variate piecewise polynomial (using a tensor product B-spline basis) with  time-dependent unknown coefficients. These coefficients are determined by imposing collocation conditions: the numerical solution is required to satisfy the PDE and boundary conditions at images of the Gauss points mapped onto certain subregions of the spatial domain. This leads to a large system of time-dependent differential algebraic equations (DAEs) which is solved using the DAE solver, DASPK. We provide numerical results in which we use the new software, called BACOL2D, to solve three test problems.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.13-13S09}, url = {http://global-sci.org/intro/article_detail/aamm/84.html} }
Copy to clipboard
The citation has been copied to your clipboard