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.

本文介绍了对 Elgindy 和 Dahy 提出的 Cole-Hopf 重心 Gegenbauer 积分伪谱 (PS) 方法 (CHBGPM) 的扩展 [使用 Cole-Hopf 重心 Gegenbauer 积分伪谱方法的粘性 Burgers 方程的高阶数值解，数学。方法应用程序。科学。41 (2018), pp. 6226–6251] 来解决 Burgers 类型的初始边界值问题，当边界函数为k在空间域的右边界定义的值在有限实数集或解域的单个/多个子域上消失。我们提出了一种新的策略，在前一种情况下比[12]中提出的计算效率更高，并且当[12]的方法无法工作时，可以在后一种情况下成功实施。此外，如果边界函数k足够平滑，则在空间和时间方向上仍然保持完全指数收敛速度。给出了与文献中其他传统方法的数值比较，以确认所提出方法的效率。包括由该方法产生的线性系统的条件数的数值研究。