Theory and Modern Applications
Table 2 Absolute errors of \(\pmb{u(t)}\) at \(\pmb{\nu=1}\) , \(\pmb{\alpha=\beta=0}\) and various choices of N for Example 1
t | N  = 3 | N  = 5 | N  = 7 | N  = 9 | N  = 11 |
|---|---|---|---|---|---|
0.0 | 5.99596⋅10−3 | 3.31436⋅10−5 | 1.06056⋅10−7 | 1.94284⋅10−10 | 7.13040⋅10−11 |
0.1 | 7.51125⋅10−4 | 1.22022⋅10−5 | 2.60870⋅10−8 | 3.37162⋅10−11 | 2.04354⋅10−11 |
0.2 | 1.25759⋅10−3 | 5.65726⋅10−6 | 3.14903⋅10−8 | 5.96878⋅10−12 | 1.63595⋅10−11 |
0.3 | 1.73337⋅10−3 | 6.86205⋅10−6 | 9.63204⋅10−10 | 3.56038⋅10−11 | 1.29785⋅10−11 |
0.4 | 1.26827⋅10−3 | 8.78068⋅10−6 | 2.68687⋅10−8 | 4.16801⋅10−11 | 4.81653⋅10−12 |
0.5 | 3.61562⋅10−4 | 1.20483⋅10−6 | 2.35946⋅10−9 | 2.76856⋅10−12 | 5.15820⋅10−12 |
0.6 | 5.63850⋅10−4 | 6.87902⋅10−6 | 2.46132⋅10−8 | 4.11042⋅10−11 | 1.03742⋅10−11 |
0.7 | 1.14646⋅10−3 | 6.87564⋅10−6 | 3.36810⋅10−9 | 2.80858⋅10−11 | 9.13957⋅10−12 |
0.8 | 1.07250⋅10−3 | 2.37780⋅10−6 | 2.54434⋅10−8 | 9.49562⋅10−12 | 6.05004⋅10−12 |
0.9 | 6.31665⋅10−5 | 8.52662⋅10−6 | 1.66859⋅10−8 | 2.98424⋅10−11 | 7.39019⋅10−12 |