B-Spline Gaussian Collocation Software for Two-Dimensional Parabolic PDEs (Advances in Applied Mathematics and Mechanics, 2021)
In this paper we describe new B-spline Gaussian collocation software for solving two-dimensionalparabolic 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 byimposing collocation conditions: the numerical solution is required to satisfy the PDEand boundary conditions at images of the Gauss points mapped onto certain subregions of the spatial domain.This leads to a large system of time-dependentdifferential 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.