Table 1 Convergence tests of the Chebyshev collocation method for representative values of governing parameters.
From: The role of a second diffusing component on the Gill–Rees stability problem
\(N\) | \(R_{S} = 500,\,\gamma = 1,\,Le = 0.5,H = 1\) | \(R_{S} = 1000,\,\gamma = 1,\,Le = 0.5,H = 1\) | \(R_{S} = 500,\,\gamma = 1,\,Le = 0.5,H = 100\) | \(R_{S} = 500,\,\gamma = 10,\,Le = 0.5,H = 1\) | \(R_{S} = 500,\,\gamma = 1,\,Le = 10,H = 1\) | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(R_{Dc}\) | \(a_{c}\) | \(c_{c}\) | \(R_{Dc}\) | \(a_{c}\) | \(c_{c}\) | \(R_{Dc}\) | \(a_{c}\) | \(c_{c}\) | \(R_{Dc}\) | \(a_{c}\) | \(c_{c}\) | \(R_{Dc}\) | \(a_{c}\) | \(c_{c}\) | |
3 | 455.15806 | 0.569400 | 0 | 904.16424 | 0.290263 | 0 | 458.54404 | 1.304487 | ± 9.624306 | 445.32753 | 0.449990 | 0 | 127.51952 | 2.236738 | ± 89.312561 |
4 | 416.98237 | 0.355783 | 0 | 829.30129 | 0.176603 | 0 | 487.79367 | 1.318743 | ± 9.639258 | 397.68067 | 0.286170 | 0 | 347.89680 | 0.279217 | ± 18.969205 |
6 | 413.72210 | 0.326146 | 0 | 824.03654 | 0.161680 | 0 | 477.92587 | 1.191875 | ± 10.015439 | 396.15973 | 0.263758 | 0 | 300.92250 | 1.057651 | ± 58.751588 |
8 | 413.59792 | 0.326841 | 0 | 823.73027 | 0.162086 | 0 | 478.10165 | 1.188263 | ± 9.954005 | 395.81154 | 0.264629 | 0 | 342.99234 | 1.226615 | ± 41.552617 |
10 | 413.56882 | 0.326854 | 0 | 823.67317 | 0.162092 | 0 | 478.12514 | 1.188081 | ± 9.952649 | 395.78540 | 0.264643 | 0 | 348.15457 | 1.715510 | ± 11.466295 |
11 | 413.57079 | 0.326850 | 0 | 823.67705 | 0.162091 | 0 | 478.12542 | 1.188079 | ± 9.952635 | 395.78690 | 0.264642 | 0 | 352.19606 | 2.164755 | 0 |
12 | 413.56977 | 0.326855 | 0 | 823.67495 | 0.162093 | 0 | 478.12567 | 1.188075 | ± 9.952608 | 395.78597 | 0.264645 | 0 | 359.16319 | 2.750712 | ± 9.071511 |
13 | 413.56964 | 0.326856 | 0 | 823.67470 | 0.162093 | 0 | 478.12576 | 1.188076 | ± 9.952607 | 395.78587 | 0.264646 | 0 | 352.87541 | 0.028388 | 0 |
14 | 413.56969 | 0.326856 | 0 | 823.67480 | 0.162093 | 0 | 478.12578 | 1.188076 | ± 9.952605 | 395.78592 | 0.264645 | 0 | 352.87541 | 0.028388 | 0 |
15 | 413.56969 | 0.326856 | 0 | 823.67480 | 0.162093 | 0 | 478.12578 | 1.188076 | ± 9.952605 | 395.78592 | 0.264645 | 0 | 352.87541 | 0.028388 | 0 |
