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

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

Year:    2023

Author:    Bernard Bialecki, Nick Fisher

International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 6 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ijnam2023-1036

International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 6 : pp. 832–854

Published online:    2023-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

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

Author Details

Bernard Bialecki

Nick Fisher