Table 2 The errors between the numerical solutions and the analytical solution at \(t=2\)
Δt and N | \(\|\nabla(\psi(x, y, t_{n})-\psi_{N}^{n})\|_{0}\) | \(\|\omega(x,y,t_{n})-\omega_{N}^{n}\|_{0}\) |
|---|---|---|
Δt = 1/8 and N = 8 | 4.4732e−2 | 3.3764e−2 |
Δt = 1/16 and N = 16 | 7.0124e−3 | 6.8274e−3 |
Δt = 1/32 and N = 32 | 9.5675e−4 | 8.9906e−4 |
Δt = 1/64 and N = 64 | 4.6703e−4 | 3.1033e−4 |