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’ typewhenthe 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.