Theory and Modern Applications
Table 1 Results with N = 256, , u(0) = 0
u(x, y, t) |
| k* | j T | err | res | res 0 |
|---|---|---|---|---|---|---|
τ = 10-3 | ||||||
σ(u) = σ 1 | ||||||
u 1 | 0.51 | 18 | 260 | 5.26(-7) | 1.51(-4) | 205.61 |
u 2 | 8.52 | 26 | 5972 | 4.81(-7) | 1.48(-4) | 51451.65 |
u 3 | 1.01 | 20 | 585 | 7.00(-7) | 1.97(-4) | 1041.69 |
u 4 | 4.01 | 24 | 1607 | 3.46(-7) | 1.13(-4) | 9617.82 |
σ(u) = σ 2 | ||||||
u 1 | 0.51 | 17 | 196 | 5.96(-7) | 1.80(-4) | 123.15 |
✔ u 2 | 145.03 | 29 | 35427 | 2.19(-7) | 9.73(-5)* | 276108.92 |
u 3 | 2.01 | 20 | 899 | 5.59(-7) | 1.71(-4) | 898.18 |
✔ u 4 | 32.01 | 25 | 3960 | 4.70(-7) | 1.85(-4)* | 31481.01 |
τ = 10-4 | ||||||
σ(u) = σ 1 | ||||||
u 1 | 0.51 | 17 | 33 | 4.22(-7) | 1.12(-4) | 89.44 |
u 2 | 8.52 | 23 | 676 | 5.40(-7) | 1.45(-4) | 6203.62 |
u 3 | 1.01 | 19 | 70 | 3.75(-7) | 9.94(-5) | 304.43 |
u 4 | 4.01 | 21 | 216 | 3.80(-7) | 1.10(-4) | 1170.79 |
σ(u) = σ 2 | ||||||
u 1 | 0.51 | 17 | 30 | 3.54(-7) | 9.63(-5) | 86.61 |
u 2 | 145.03 | 25 | 7160 | 4.65(-7) | 1.55(-4) | 28054.93 |
u 3 | 2.01 | 19 | 115 | 4.00(-7) | 1.10(-4) | 297.76 |
u 4 | 32.01 | 22 | 852 | 4.43(-7) | 1.53(-4) | 3266.07 |
σ(u) = σ 3 | ||||||
u 2 | 1.50 | 22 | 1534 | 4.19(-7) | 1.30(-4) | 3061.65 |
u 3 | 100.00 | 19 | 1515 | 3.16(-7) | 1.10(-4) | 297.96 |
u 4 | 100.00 | 20 | 1986 | 2.67(-7) | 1.06(-4) | 558.51 |