“…In dealing with the problem of numerically solving the convection–diffusion equation, several techniques have been applied such as finite differences, finite elements, boundary elements and meshless methods. Comprehensive studies and extensive lists of works using finite differences and finite elements can be found in references (Lewis et al , 2004; Nithiarasu et al , 2016; Yu and Heinrich, 1987) and Li (1990), while for boundary elements, the papers (Taigbenu and Liggett, 1986; Tanaka et al , 1987; Al-Bayati and Wrobel, 2018b; Al-Bayati and Wrobel, 2018a; Tanaka and Honma, 1989; Al-Bayati and Wrobel, 2019; Al-Bayati, 2018; Al-Bayati and Wrobel, 2020; Azis, 2019; Chen and Wang, 2016) and Peng et al (2020), refer to the majority of works done on the subject. The motivation to work on boundary elements resides in the fact that when applying the first two mentioned approaches, several numerical problems such as oscillations and smoothing of wave fronts have been reported.…”