A Domain Decomposition Chebyshev Spectral Collocation Method for Volterra Integral Equations (Journal of Mathematical Study, 2019)
We develop a domain decomposition Chebyshev spectral collocation methodfor the second-kind linear and nonlinear Volterra integral equations with smooth kernelfunctions. The method is easy to implement and possesses high accuracy. In theconvergence analysis, we derive the spectral convergence order under the $L^∞$-normwithout the Chebyshev weight function, and we also show numerical examples whichcoincide with the theoretical analysis.
Keywords: Nonlinear Volterra integral equations; domain decomposition method; Chebyshev–collocation spectral method; convergence analysis.