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B-Spline Gaussian Collocation Software for Two-Dimensional Parabolic PDEs

Published online by Cambridge University Press:  03 June 2015

Zhi Li  and
Paul Muir
Zhi Li*
Affiliation:
Mathematics and Computing Science, Saint Mary’s University, Halifax, Nova Scotia, Canada B3H 3C3
Paul Muir*
Affiliation:
Mathematics and Computing Science, Saint Mary’s University, Halifax, Nova Scotia, Canada B3H 3C3
*
Email: lizhiupc@gmail.com
Corresponding author. Email: muir@smu.ca
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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

65M2065M70CollocationB-splinestwo-dimensional partial differential equationsdifferential-algebraic equations
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 5 , Special Issue 4 , August 2013 , pp. 528 - 547
Copyright
Copyright © Global-Science Press 2013

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