Cubic spline wavelets with complementary boundary conditions

被引：17

作者：

Cerna, Dana ^{[1
]}

Finek, Vaclav ^{[1
]}

机构：

[1] Tech Univ Liberec, Dept Math & Didact Math, Liberec 46117, Czech Republic

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2012年 / 219卷 / 04期

关键词：

Wavelet; Cubic spline; Complementary boundary conditions; Homogeneous Dirichlet boundary conditions; Condition number; FREDHOLM INTEGRAL-EQUATIONS; CONVERGENCE-RATES; INTERVAL; DECOMPOSITION; SPACES; BASES;

D O I：

10.1016/j.amc.2012.08.027

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose a new construction of a stable cubic spline-wavelet basis on the interval satisfying complementary boundary conditions of the second order. It means that the primal wavelet basis is adapted to homogeneous Dirichlet boundary conditions of the second order, while the dual wavelet basis preserves the full degree of polynomial exactness. We present quantitative properties of the constructed bases and we show superiority of our construction in comparison to some other known spline wavelet bases in an adaptive wavelet method for the partial differential equation with the biharmonic operator. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：1853 / 1865

页数：13

共 28 条

[1]

BITTNER K, 2006, WAVELETS SPLINES ATH, P93

[2] A fast wavelet-multigrid method to solve elliptic partial differential equations [J].

Bujurke, N. M. ;

Salimath, C. S. ;

Kudenatti, R. B. ;

Shiralashetti, S. C. .

APPLIED MATHEMATICS AND COMPUTATION, 2007, 185 (01) :667-680

[3] Local decomposition of refinable spaces and wavelets [J].

Carnicer, JM ;

Dahmen, W ;

Pena, JM .

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 1996, 3 (02) :127-153

[4]

Cerna D., APPROXIMATE MU UNPUB

[5]

Cerná D, 2008, AIP CONF PROC, V1048, P134, DOI 10.1063/1.2990873

[6] Adaptive Wavelet Method for Fourth-Order Elliptic Problems [J].

Cerna, Dana ;

Finek, Vaclav .

NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS A-C, 2011, 1389

[7] Construction of optimally conditioned cubic spline wavelets on the interval [J].

Cerna, Dana ;

Finek, Vaclav .

ADVANCES IN COMPUTATIONAL MATHEMATICS, 2011, 34 (02) :219-252

[8] Solving diffusion equation using wavelet method [J].

Chen, Xuefeng ;

Xiang, Jiawei .

APPLIED MATHEMATICS AND COMPUTATION, 2011, 217 (13) :6426-6432

[9]

CHUI CK, 1992, INT S NUM M, V105, P53

[10]

Cohen A, 2001, MATH COMPUT, V70, P27, DOI 10.1090/S0025-5718-00-01252-7

← 1 2 3 →