摘要
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.
