ORTHOGONAL SPLINE COLLOCATION FOR POISSON'S EQUATION WITH NEUMANN BOUNDARY CONDITIONS

被引：0

作者：

Bialecki, Bernard ^{[1
]}

Fisher, Nick ^{[2
]}

机构：

[1] Colorado Sch Mines, Dept Appl Math & Stat, Golden, CO 80401 USA

[2] Portland State Univ, Dept Math & Stat, Portland, OR 97201 USA

来源：

INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING | 2023年 / 20卷 / 06期

关键词：

Poisson's equation; Neumann boundary conditions; orthogonal spline collocation; convergence analysis; matrix decomposition algorithm;

D O I：

10.4208/ijnam2023-1036

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：832 / 854

页数：23

共 50 条

[1] Superconvergence of the orthogonal spline collocation solution of Poisson's equation
Bialecki, B
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 1999, 15 (03) : 285 - 303
[2] Symmetrization of Poisson's equation with Neumann boundary conditions
Langford, Jeffrey J.
ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 2015, 14 (04) : 1025 - 1063
[3] Tensorial basis spline collocation method for Poisson's equation
Plagne, L
Berthou, JY
JOURNAL OF COMPUTATIONAL PHYSICS, 2000, 157 (02) : 419 - 440
[4] Modified nodal cubic spline collocation for Poisson's equation
Abushama, Abeer Ali
Bialecki, Bernard
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2008, 46 (01) : 397 - 418
[5] Orthogonal spline collocation methods for the subdiffusion equation
Li, Can
Zhao, Tinggang
Deng, Weihua
Wu, Yujiang
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2014, 255 : 517 - 528
[6] Optimal preconditioners on solving the Poisson equation with Neumann boundary conditions
Lee, Byungjoon
Min, Chohong
JOURNAL OF COMPUTATIONAL PHYSICS, 2021, 433
[7] The Crank-Nicolson Hermite Cubic Orthogonal Spline Collocation Method for the Heat Equation with Nonlocal Boundary Conditions
Bialecki, B.
Fairweather, G.
Lopez-Marcos, J. C.
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2013, 5 (04) : 442 - 460
[8] Analysis of a multigrid method for solving Poisson's equation with full Neumann boundary conditions
Mohamed, S.A.
2003, Cairo University (50):
[9] Very weak solutions of Poisson’s equation with singular data under Neumann boundary conditions
Jochen Merker
Jean-Michel Rakotoson
Calculus of Variations and Partial Differential Equations, 2015, 52 : 705 - 726
[10] Very weak solutions of Poisson's equation with singular data under Neumann boundary conditions
Merker, Jochen
Rakotoson, Jean-Michel
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2015, 52 (3-4) : 705 - 726

← 1 2 3 4 5 →