期刊文献+

两点边值问题的小波配点法 被引量:8

A wavelet collocation method for solving two-point boundary value problems
下载PDF
导出
摘要 根据多分辨分析,提出用任意连续的尺度函数构造区间上的插值基函数,形成以尺度函数为基础的求解两点边值问题的小波配点法。该方法中,尺度函数不受紧支撑、插值等性质的限制,计算复杂度小,数值解收敛性由多分辨分析理论保证。同时,给出边值条件的积分处理方法,能够方便地处理任意边界条件,当尺度函数不具有高阶导数时,该方法也能有效使用。数值算例表明,该方法是一个高效、高精度的算法。 Based on multi-resolution analysis, a wavelet collocation method of solving two-point bounda- ry value problem using scaling function is proposed in this paper. The interpolation base functions in interval of the collocation method are formed by using arbitrary continuous scaling function, but the scaling function itself dose not required the properties of compact support, interpolation and so on. The computational complexity of this method is low, and the convergence is ensured by multi-resolution analysis theory. At the same time, an integral approach of dealing with boundary condition is suggested, which can handle arbitrary boundary condition conveniently. As the scaling function has no high-order derivative, the method can be used effectively. Numerical example indicates that the method is a highly efficient and accurate algorithm.
出处 《计算力学学报》 EI CAS CSCD 北大核心 2009年第6期947-950,955,共5页 Chinese Journal of Computational Mechanics
基金 陕西省教育厅科学研究计划(08JK395) 西安理工大学高学历人员科研基金资助项目
关键词 多分辨分析 尺度函数 小波配点法 对流占优方程 multi-resolution analysis scaling function wavelet-collocation method convection-dominated equation
  • 相关文献

参考文献7

  • 1BERTOLUZZI S, NAIDI G. A wavelet collocation method for the numerical solution of partial differential equations[j]. Applied and Computational Harmonic Analysis, 1996,3(1) : 1-9.
  • 2COMINCIOLI V, NALDI G, SCAPOLLA T. A wavelet-based method for numerical solution of nonlinear evolution equations[J]. Applied Numerical Mathematics, 2000,33(1-4) :291-297.
  • 3ADROVER A, CONTINILLO G, CRESCITELLI S, et al. Wavelet-like collocation method for finite-dimensional reduction of distributed systems[J]. Computers & Chemical Engineering,2000,24(12) :2687- 2703.
  • 4YU S, ZHAO S, WEI G W. Local spectral time splitting method for first-and second-order partial differential equations[J]. Journal of Computational Physics, 2005,206(2) : 727-780.
  • 5SHEN You-jian, LIN Wei. Collocation method for the natural boundary integral equation[J]. Applied Mathematics Letters, 2006,19P( 11 ) : 1278-1285.
  • 6VASILYEV O V, PAOLUCCI S, SEN M. A multilevel wavelet collocation method for solving partial differential equations in a finite domain[J]. Journal of Computational Physics, 1995,120(1) : 33-47.
  • 7徐长发,张锴,陈端,闵志方.两点边值问题Daubechies小波δ-序列数值解法[J].华中科技大学学报(自然科学版),2006,34(5):40-42. 被引量:2

二级参考文献4

共引文献1

同被引文献64

引证文献8

二级引证文献20

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部