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

Author:

Li Zhi,Muir Paul

Abstract

AbstractIn this paper we describe newB-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 productB-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.

Publisher

Global Science Press

Subject

Applied Mathematics,Mechanical Engineering

Reference14 articles.

Cited by 6 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Superconvergent interpolants for Gaussian collocation solutions of mixed order BVODE systems;AIMS Mathematics;2022

2. Error control Gaussian collocation software for boundary value ODEs and 1D time-dependent PDEs;Numerical Algorithms;2019-06-06

3. Performance analysis of error-control B-spline Gaussian collocation software for PDEs;Computers & Mathematics with Applications;2019-04

4. Extended BACOLI;ACM Transactions on Mathematical Software;2019-03-31

5. Algorithm 962;ACM Transactions on Mathematical Software;2016-06-15

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