TY - JOUR
T1 - Orthogonal Spline Collocation for Poisson’s Equation with Neumann Boundary Conditions
AU - Bialecki , Bernard
AU - Fisher , Nick
JO - International Journal of Numerical Analysis and Modeling
VL - 6
SP - 832
EP - 854
PY - 2023
DA - 2023/11
SN - 20
DO - http://doi.org/10.4208/ijnam2023-1036
UR - https://global-sci.org/intro/article_detail/ijnam/22143.html
KW - Poisson’s equation, Neumann boundary conditions, orthogonal spline collocation, convergence analysis, matrix decomposition algorithm.
AB - <p style="text-align: justify;">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.</p>