An ultraspherical spectral method for linear Fredholm and Volterra integro-differential equations of convolution type
Numerical Analysis
2017-12-04 v1
Abstract
The Legendre-based ultraspherical spectral method for ordinary differential equations is combined with a formula for the convolution of two Legendre series to produce a new technique for solving linear Fredholm and Volterra integro-differential equations with convolution-type kernels. When the kernel and coefficient functions are sufficiently smooth then the method is spectrally-accurate and the resulting almost-banded linear systems can be solved with linear complexity.
Keywords
Cite
@article{arxiv.1712.00304,
title = {An ultraspherical spectral method for linear Fredholm and Volterra integro-differential equations of convolution type},
author = {Nicholas Hale},
journal= {arXiv preprint arXiv:1712.00304},
year = {2017}
}