Trigonometric Hermite wavelet approximation for the integral equations of second kind with weakly singular kernel

Authors:
Jing Gao;Yao-Lin Jiang
Affiliations:
Department of Mathematical Sciences, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, PR China;Department of Mathematical Sciences, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 7
Cited 3

A fast algorithm for particle simulations

Journal of Computational Physics
A fast numerical solution for a second kind boundary integral equation with a logarithmic kernel

SIAM Journal on Numerical Analysis
On the numerical solution of a logarithmic integral equation of the first kind for the Helmholtz equation

Numerische Mathematik
Trigonometric wavelets for Hermite interpolation

Mathematics of Computation
Integral Operators on Sparse Grids

SIAM Journal on Numerical Analysis
A note on wave number dependence of wavelet matrix compression for integral equations with oscillatory kernel

Journal of Computational and Applied Mathematics
A two-dimensional wavelet-packet transform for matrix compression of integral equations with highly oscillatory kernel

Journal of Computational and Applied Mathematics

Existence and uniqueness of nontrivial collocation solutions of implicitly linear homogeneous Volterra integral equations

Journal of Computational and Applied Mathematics
Finite element analysis of beam structures based on trigonometric wavelet

Finite Elements in Analysis and Design
New algorithms for the numerical solution of nonlinear Fredholm and Volterra integral equations using Haar wavelets

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.29

Visualization

Abstract

This paper is concerned with a trigonometric Hermite wavelet Galerkin method for the Fredholm integral equations with weakly singular kernel. The kernel function of this integral equation considered here includes two parts, a weakly singular kernel part and a smooth kernel part. The approximation estimates for the weakly singular kernel function and the smooth part based on the trigonometric Hermite wavelet constructed by E. Quak [Trigonometric wavelets for Hermite interpolation, Math. Comp. 65 (1996) 683-722] are developed. The use of trigonometric Hermite interpolant wavelets for the discretization leads to a circulant block diagonal symmetrical system matrix. It is shown that we only need to compute and store O(N) entries for the weakly singular kernel representation matrix with dimensions N^2 which can reduce the whole computational cost and storage expense. The computational schemes of the resulting matrix elements are provided for the weakly singular kernel function. Furthermore, the convergence analysis is developed for the trigonometric wavelet method in this paper.