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

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  • 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, differentialalgebraic equations.

  • AMS Subject Headings

65M20, 65M70

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-5-528, author = {}, 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} }
TY - JOUR T1 - B-Spline Gaussian Collocation Software for Two-Dimensional Parabolic PDEs JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 528 EP - 547 PY - 2013 DA - 2013/08 SN - 5 DO - http://doi.org/10.4208/aamm.13-13S09 UR - https://global-sci.org/intro/article_detail/aamm/84.html KW - Collocation, B-splines, two-dimensional partial differential equations, differentialalgebraic equations. AB -

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.

Zhi Li & Paul Muir. (1970). B-Spline Gaussian Collocation Software for Two-Dimensional Parabolic PDEs. Advances in Applied Mathematics and Mechanics. 5 (4). 528-547. doi:10.4208/aamm.13-13S09
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