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This paper presents an extension to the Cole–Hopf barycentric Gegenbauer integral pseudospectral (PS) method (CHBGPM) presented in Elgindy and Dahy [ High-order numerical solution of viscous Burgers' equation using a Cole–Hopf barycentric Gegenbauer integral pseudospectral method , Math. Methods Appl. Sci. 41 (2018), pp. 6226–6251] to solve an initial-boundary value problem of Burgers' type when the boundary function  k  defined at the right boundary of the spatial domain vanishes at a finite set of real numbers or on a single/multiple subdomain(s) of the solution domain. We present a new strategy that is computationally more efficient than that presented in [12] in the former case, and can be implemented successfully in the latter case when the method of [12] fails to work. Moreover, fully exponential convergence rates are still preserved in both spatial and temporal directions if the boundary function  k  is sufficiently smooth. Numerical comparisons with other traditional methods in the literature are presented to confirm the efficiency of the proposed method. A numerical study of the condition number of the linear systems produced by the method is included.

High-order numerical solution of viscous Burgers' equation using an extended Cole–Hopf barycentric Gegenbauer integral pseudospectral method