Iterated fast multiscale Galerkin methods for Fredholm integral equations of second kind with weakly singular kernels

Authors:
Guangqing Long;Gnaneshwar Nelakanti;Xiaohua Zhang
Affiliations:
Department of Mathematics, Guangxi Normal College, Nanning 530001, PR China;Department of Mathematics, Indian Institute of Technology, Kharagpur, 721302, West Bengal, India;Department of Mathematics, Guangxi Normal College, Nanning 530001, PR China
Venue:
Applied Numerical Mathematics
Year:
2012

Citing 13
Cited 0

Gauss-type quadratures for weakly singular integrals and their application to Fredholm integral equations of the second kind

Mathematics of Computation
Wavelet Galerkin methods for second-kind integral equations

Journal of Computational and Applied Mathematics - Special issue: dedicated to William B. Gragg on the occasion of his 60th Birthday
Fast Collocation Methods for Second Kind Integral Equations

SIAM Journal on Numerical Analysis
An Implementation of Fast Wavelet Galerkin Methods for Integral Equations of the Second Kind

Journal of Scientific Computing
Iteration methods for Fredholm integral equations of the second kind

Computers & Mathematics with Applications
A Fast Fourier-Galerkin Method for Solving Singular Boundary Integral Equations

SIAM Journal on Numerical Analysis
A fast solver for a hypersingular boundary integral equation

Applied Numerical Mathematics
A fast Petrov-Galerkin method for solving the generalized airfoil equation

Journal of Complexity
A meshless based method for solution of integral equations

Applied Numerical Mathematics
Numerical solution of the higher-order linear Fredholm integro-differential-difference equation with variable coefficients

Computers & Mathematics with Applications
The multi-projection method for weakly singular Fredholm integral equations of the second kind

International Journal of Computer Mathematics
Numerical solution for the weakly singular Fredholm integro-differential equations using Legendre multiwavelets

Journal of Computational and Applied Mathematics
The spectral methods for parabolic Volterra integro-differential equations

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We propose iterated fast multiscale Galerkin methods for the second kind Fredholm integral equations with mildly weakly singular kernel by combining the advantages of fast methods and iteration post-processing methods. To study the super-convergence of these methods, we develop a theoretical framework for iterated fast multiscale schemes, and apply the scheme to integral equations with weakly singular kernels. We show theoretically that even the computational complexity is almost optimal, our schemes improve the accuracy of numerical solutions greatly, and exhibit the global super-convergence. Numerical examples are presented to illustrate the theoretical results and the efficiency of the methods.