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Volume 20, Issue 6
Orthogonal Spline Collocation for Poisson’s Equation with Neumann Boundary Conditions

Bernard Bialecki & Nick Fisher

DOI: 10.4208/ijnam2023-1036

Int. J. Numer. Anal. Mod., 20 (2023), pp. 832-854.

Published online: 2023-11

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  • 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.

  • Keywords

Poisson’s equation, Neumann boundary conditions, orthogonal spline collocation, convergence analysis, matrix decomposition algorithm.

  • AMS Subject Headings

65F05, 65N15, 65N35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-20-832, author = {Bialecki , Bernard and Fisher , Nick}, title = {Orthogonal Spline Collocation for Poisson’s Equation with Neumann Boundary Conditions}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2023}, volume = {20}, number = {6}, pages = {832--854}, 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.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2023-1036}, url = {http://global-sci.org/intro/article_detail/ijnam/22143.html} }
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 -

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.

Bernard Bialecki & Nick Fisher. (2023). Orthogonal Spline Collocation for Poisson’s Equation with Neumann Boundary Conditions. International Journal of Numerical Analysis and Modeling. 20 (6). 832-854. doi:10.4208/ijnam2023-1036
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