Table 3 Numerical solution and pattern of Experiments 2–3 with different initial condition of Figs. 5–11
Figure | η(x,y,0) | u(x,y,0) | v(x,y,0) |
|---|---|---|---|
Fig. 5 | \(\sec h(\sin (y{x^{2}}))\) | \(\sec h(50x^{2}+200y-9)+\operatorname{ones}(N)\) | \(\frac{4}{5}\sin (\cos ({y^{2}}-{x^{2}}))\) |
Fig. 6 | \(\sin (\sec h(\frac{x^{2}}{2}- {y^{2}})) + \frac{1}{2}\) | \(\sin (\cos (\frac{x^{2}}{2} + {y^{2}})) + \frac{1}{2}\) | \(-\sin ( {x^{2}}+\frac{y^{2}}{10})\) |
Fig. 7 | \(\sec h(\frac{x}{2} + {y^{3}})\) | \(\cos ({x^{2}} + {y^{2}})\) | \(\sin (50x^{2}+200y-9)\) |
Fig. 8 | \(-\frac{1}{10}\sin ( \frac{x^{2}+y^{2}}{10})\) | \(\cos (e^{-\sin ({x^{2}}+{y^{2}})})\) | \(\sec h(\sec h({x^{2}}+y))\) |
Fig. 9 | \(\frac{1}{10}\sin (\frac{y^{2}-x^{2}}{10})\) | \(\pi \sin (50x^{2}-{y^{2}})+\frac{3}{5}\operatorname{rand}(N)\) | \(\cos (x+\frac{y^{2}}{10})\) |
Fig. 10 | \(-\sin ( 10x^{2}+\frac{y^{2}}{10})\) | \(-\sin ( \pi ({(x-\frac{2}{5})^{3}}+{(y +\frac{2}{5})^{2}}))\) | \(\sin (-{x^{2}}+\frac{y^{2}}{10})\) |
Fig. 11 | \(\sin (50x^{2}+200y-9)\) | \(\cos (\pi ({(x-\frac{2}{5})^{2}}+{(y+\frac{2}{5})^{2}}))+\sec h(20({(x+\frac{2}{5})^{2}}+{(y-\frac{2}{5})^{2}}))\) | \(\sin (\pi (-{x^{2}}+{y^{2}}))\) |