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@article{Gutleb:2020:10.1137/19M1267441,
author = {Gutleb, T and Olver, S},
doi = {10.1137/19M1267441},
journal = {SIAM Journal on Numerical Analysis},
pages = {1993--2018},
title = {A sparse spectral method for Volterra integral equations using orthogonal polynomials on the triangle},
url = {http://dx.doi.org/10.1137/19M1267441},
volume = {58},
year = {2020}
}

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TY  - JOUR
AB  - We introduce and analyze a sparse spectral method for the solution of Volterra integral equations using bivariate orthogonal polynomials on a triangle domain. The sparsity of  the Volterra operator on a weighted Jacobi basis is used to achieve high efficiency and exponential convergence. The discussion is followed by a demonstration of the method on example Volterra  integral equations of the first and second kind with or without known analytic solutions as well as an application-oriented numerical experiment. We prove convergence for both first and second kindproblems, where the former builds on connections with Toeplitz operators.
AU  - Gutleb,T
AU  - Olver,S
DO  - 10.1137/19M1267441
EP  - 2018
PY  - 2020///
SN  - 0036-1429
SP  - 1993
TI  - A sparse spectral method for Volterra integral equations using orthogonal polynomials on the triangle
T2  - SIAM Journal on Numerical Analysis
UR  - http://dx.doi.org/10.1137/19M1267441
UR  - https://epubs.siam.org/doi/10.1137/19M1267441
UR  - http://hdl.handle.net/10044/1/79585
VL  - 58
ER  -

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