A Domain Decomposition Chebyshev Spectral Collocation Method for Volterra Integral Equations

Abstract

We develop a domain decomposition Chebyshev spectral collocation method for the second-kind linear and nonlinear Volterra integral equations with smooth kernel functions. The method is easy to implement and possesses high accuracy. In the convergence analysis, we derive the spectral convergence order under the $L^∞$-norm without the Chebyshev weight function, and we also show numerical examples which coincide with the theoretical analysis.