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

IF 1.3 4区数学 Q1 MATHEMATICS

International Journal of Numerical Analysis and Modeling Pub Date : 2023-06-01 DOI:10.4208/ijnam2023-1036

Bernard Bialecki null, Nick Fisher

引用次数: 0

Abstract

. We apply orthogonal spline collocation with splines of degree r (cid:21) 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 e(cid:14)ciently the approximate solution using a matrix decomposition algorithm involving the solution of a symmetric generalized eigenvalue problem.

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具有Neumann边界条件的Poisson方程的正交样条配置

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来源期刊

International Journal of Numerical Analysis and Modeling 数学-数学

CiteScore

2.10

自引率

9.10%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal is directed to the broad spectrum of researchers in numerical methods throughout science and engineering, and publishes high quality original papers in all fields of numerical analysis and mathematical modeling including: numerical differential equations, scientific computing, linear algebra, control, optimization, and related areas of engineering and scientific applications. The journal welcomes the contribution of original developments of numerical methods, mathematical analysis leading to better understanding of the existing algorithms, and applications of numerical techniques to real engineering and scientific problems. Rigorous studies of the convergence of algorithms, their accuracy and stability, and their computational complexity are appropriate for this journal. Papers addressing new numerical algorithms and techniques, demonstrating the potential of some novel ideas, describing experiments involving new models and simulations for practical problems are also suitable topics for the journal. The journal welcomes survey articles which summarize state of art knowledge and present open problems of particular numerical techniques and mathematical models.