Orthogonal Spline Collocation for Poisson’s Equation with Neumann Boundary Conditions

Abstract

We apply orthogonal spline collocation with splines of degree $r ≥ 3$ to solve, on the unit square, Poisson’s equation with Neumann boundary conditions. We show that the $H^1$ norm error is of order $r$ and explain how to compute efficiently the approximate solution using a matrix decomposition algorithm involving the solution of a symmetric generalized eigenvalue problem.