An ℎ𝑝-spectral collocation method for nonlinear Volterra integral equations with vanishing variable delays

Zhong-qing, Wang; Chang-tao, Sheng

doi:10.1090/mcom/3023

An $hp$-spectral collocation method for nonlinear Volterra integral equations with vanishing variable delays
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by Wang Zhong-qing and Sheng Chang-tao PDF

Math. Comp. 85 (2016), 635-666 Request permission

Abstract:

In this paper, we propose a multistep Legendre-Gauss spectral collocation method for nonlinear second-kind Volterra integral equations (VIEs) with vanishing variable delays. This method is easy to implement and possesses high-order accuracy. We also provide a rigorous convergence analysis of the $hp$-version of the multistep spectral collocation method under $L^2$-norm. Numerical results confirm the theoretical predictions.

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