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Int. J. Numer. Anal. Mod., 20 (2023), pp. 832-854.
Published online: 2023-11
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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.
}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2023-1036}, url = {http://global-sci.org/intro/article_detail/ijnam/22143.html} }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.