UBC Theses and Dissertations
A supra-convergent scheme for the solution of differential equations on an arbitrary mesh Scott, Karen
This thesis describes a compact numerical scheme to solve second-order linear differential equations with Dirichlet boundary conditions on arbitrary meshes. The scheme uses a staggered grid to achieve second-order accuracy on a nonuniform mesh. Regular and singularly perturbed problems in one and higher dimensions are considered. Numerical experiments are presented which support the theoretical results. The methods presented are also applicable to equations with other types of boundary conditions, and to nonlinear and higher-order differential equations.