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

[21] Wavelet bases of Hermite cubic splines on the interval [J].

Jia, RQ ;

Liu, ST .

ADVANCES IN COMPUTATIONAL MATHEMATICS, 2006, 25 (1-3) :23-39

[22] Graded Galerkin Methods for the High-Order Convection-Diffusion Problem [J].

Liu, Song-Tao ;

Xu, Yuesheng .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2009, 25 (06) :1261-1282

[23] Numerical solution of the integral equation of the second kind by using wavelet bases of Hermite cubic splines [J].

Maleknejad, K. ;

Yousefi, M. .

APPLIED MATHEMATICS AND COMPUTATION, 2006, 183 (01) :134-141

[24] Filter matrix based on interpolation wavelets for solving Fredholm integral equations [J].

Maleknejad, K. ;

Khademi, A. .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2011, 16 (11) :4197-4207

[25] The method of moments for solution of second kind Fredholm integral equations based on B-spline wavelets [J].

Maleknejad, K. ;

Sahlan, M. Nosrati .

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2010, 87 (07) :1602-1616

[26] New Stable Biorthogonal Spline-Wavelets on the Interval [J].

Primbs, Miriam .

RESULTS IN MATHEMATICS, 2010, 57 (1-2) :121-162

[27] Wavelet based schemes for linear advection-dispersion equation [J].

Sandeep, K. ;

Gaur, Shikha ;

Dutta, D. ;

Kushwaha, H. S. .

APPLIED MATHEMATICS AND COMPUTATION, 2011, 218 (07) :3786-3798

[28] Biorthogonal Cubic Hermite Spline Multiwavelets on the Interval with Complementary Boundary Conditions [J].

Schneider, Andreas .

RESULTS IN MATHEMATICS, 2009, 53 (3-4) :407-416

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