Research Article
A Single Sweep AGE Algorithm on a Variable Mesh Based on Off-Step Discretization for the Solution of Nonlinear Burgers’ Equation
| | TAGE | Single sweep AGE | MAE | RMS errors | | | Iter | | | Iter |
| | 10 | 0.0368 | 0.0373 | 8 | 0.050 | 0.052 | 5 | 0.8036(−03) | 0.2692(−03) | 20 | 0.0329 | 0.0334 | 9 | 0.034 | 0.046 | 6 | 0.7645(−03) | 0.1770(−03) | 30 | 0.0297 | 0.0311 | 10 | 0.017 | 0.034 | 7 | 0.7605(−03) | 0.1436(−03) | 40 | 0.0283 | 0.0287 | 10 | 0.023 | 0.0242 | 8 | 0.7602(−03) | 0.1243(−03) | 50 | 0.0261 | 0.0269 | 10 | 0.025 | 0.027 | 8 | 0.7602(−03) | 0.1112(−03) | 60 | 0.0242 | 0.0251 | 10 | 0.0211 | 0.0218 | 9 | 0.7602(−03) | 0.1015(−03) |
| | 10 | 0.0554 | 0.0562 | 7 | 0.0555 | 0.0559 | 5 | 0.6954(−03) | 0.2261(−03) | 20 | 0.0457 | 0.0464 | 9 | 0.035 | 0.037 | 7 | 0.4545(−03) | 0.1034(−04) | 30 | 0.0403 | 0.0412 | 10 | 0.027 | 0.029 | 8 | 0.4245(−03) | 0.7896(−04) | 40 | 0.0381 | 0.0393 | 10 | 0.025 | 0.030 | 9 | 0.4198(−03) | 0.6765(−04) | 50 | 0.0359 | 0.0364 | 10 | 0.03 | 0.033 | 9 | 0.4191(−03) | 0.6040(−04) | 60 | 0.0326 | 0.0335 | 10 | 0.022 | 0.029 | 10 | 0.4190(−03) | 0.5512(−04) |
| | 10 | 0.0204 | 0.0211 | 8 | 0.016 | 0.020 | 7 | 0.8035(−03) | 0.3961(−03) | 20 | 0.0183 | 0.0189 | 8 | 0.011 | 0.014 | 6 | 0.5906(−03) | 0.1492(−03) | 30 | 0.0079 | 0.0084 | 9 | 0.007 | 0.0072 | 7 | 0.5252(−03) | 0.1101(−03) | 40 | 0.0056 | 0.0067 | 11 | 0.0051 | 0.0052 | 9 | 0.5044(−03) | 0.9227(−04) | 50 | 0.0036 | 0.0041 | 15 | 0.0043 | 0.0043 | 12 | 0.4973(−03) | 0.8159(−04) | 60 | 0.0034 | 0.0035 | 17 | 0.0032 | 0.0034 | 16 | 0.4949(−03) | 0.7419(−04) |
| | 10 | 0.0198 | 0.0211 | 8 | 0.016 | 0.017 | 7 | 0.4542(−03) | 0.3755(−03) | 20 | 0.0172 | 0.0181 | 8 | 0.011 | 0.018 | 6 | 0.6976(−04) | 0.4929(−04) | 30 | 0.0069 | 0.0072 | 9 | 0.007 | 0.008 | 7 | 0.4018(−04) | 0.2422(−04) | 40 | 0.0064 | 0.0064 | 10 | 0.0065 | 0.0057 | 8 | 0.3333(−04) | 0.1789(−04) | 50 | 0.0045 | 0.0043 | 13 | 0.0036 | 0.0041 | 12 | 0.3124(−04) | 0.1525(−04) | 60 | 0.0035 | 0.0034 | 17 | 0.0043 | 0.0033 | 15 | 0.3054(−04) | 0.1372(−04) |
| | 10 | 0.0174 | 0.0177 | 10 | 0.01 | 0.027 | 8 | 0.1217(−02) | 0.5654(−03) | 20 | 0.009 | 0.011 | 12 | 0.0113 | 0.0115 | 9 | 0.1044(−03) | 0.4913(−04) | 30 | 0.0063 | 0.0065 | 14 | 0.0072 | 0.0077 | 10 | 0.4547(−04) | 0.1367(−04) | 40 | 0.0063 | 0.0069 | 16 | 0.0054 | 0.0056 | 11 | 0.2617(−04) | 0.6119(−05) | 50 | 0.0042 | 0.0046 | 18 | 0.0044 | 0.0045 | 12 | 0.1697(−04) | 0.3416(−05) | 60 | 0.0034 | 0.0039 | 21 | 0.0032 | 0.0041 | 13 | 0.1188(−04) | 0.2152(−05) |
| | 10 | 0.017 | 0.025 | 9 | 0.015 | 0.026 | 7 | 0.1234(−02) | 0.5767(−03) | 20 | 0.0101 | 0.011 | 11 | 0.0118 | 0.0118 | 9 | 0.1058(−03) | 0.4505(−04) | 30 | 0.0071 | 0.0083 | 13 | 0.0075 | 0.0075 | 10 | 0.2644(−04) | 0.1025(−04) | 40 | 0.0054 | 0.0063 | 15 | 0.0049 | 0.0058 | 11 | 0.1502(−04) | 0.3813(−05) | 50 | 0.0043 | 0.0049 | 17 | 0.0038 | 0.0049 | 12 | 0.9686(−05) | 0.1870(−05) | 60 | 0.0035 | 0.004 | 20 | 0.0042 | 0.0044 | 11 | 0.6762(−05) | 0.1084(−05) |
|
|