Table 3 \(H=\frac{1}{24},\ h=\tau \)
From: Parallel algorithm for convection–diffusion system based on least-squares procedure
h | m | \(a=1\) | \(a=1\) e–2 | \(a=1e{-}4\) | |||
|---|---|---|---|---|---|---|---|
\(\Vert \cdot \Vert _2\) | \(\Vert \cdot \Vert _\infty \) | \(\Vert \cdot \Vert _2\) | \(\Vert \cdot \Vert _\infty \) | \(\Vert \cdot \Vert _2\) | \(\Vert \cdot \Vert _\infty \) | ||
\(\frac{1}{48}\) | \(*\) | \(2.9866\) e–2 | \(1.9250\) e–1 | \(8.6118e{-}3\) | \(2.6493\) e–2 | \(7.4344e{-}3\) | \(1.5421\) e–2 |
\(\frac{1}{48}\) | 1 | \( 2.0573\) e–1 | \(4.6896\) e–1 | \(9.1964e{-}3\) | \( 2.8774\) e–2 | \(8.0709e{-}3\) | \(2.1458\) e–2 |
\(\frac{1}{48}\) | 2 | \(2.0179 \) e–1 | \(4.5896\) e–1 | \(8.9982e{-}3 \) | \(2.1092 \) e–2 | \(7.6579e{-}3\) | \(1.5340\) e–2 |
\(\frac{1}{48}\) | 3 | \(2.0061 \) e–1 | \(4.5878\) e–1 | \(9.0836e{-}3 \) | \(2.2172 \) e–2 | \(7.6797e{-}3\) | \(1.5379\) e–2 |
\(\frac{1}{48}\) | 4 | \(1.9834 \) e–1 | \(4.5297\) e–1 | \(9.1164e{-}3 \) | \(2.2495 \) e–2 | \(7.6884e{-}3\) | \(1.5387\) e–2 |
\(\frac{1}{96}\) | \(*\) | \(1.4800e{-}2\) | \(9.5488e{-}2\) | \( 4.9541e{-}3\) | \(2.5220e{-}2\) | \(3.6348e{-}3\) | \(7.4154e{-}3\) |
\(\frac{1}{96}\) | 1 | \(1.1518\) e–1 | \(2.8223\) e–1 | \(4.8606e{-}3\) | \(2.3682e{-}2\) | \(3.6679e{-}3\) | \(7.6455e{-}3\) |
\(\frac{1}{96}\) | 2 | \(1.1342\) e–1 | \(2.7485\) e–1 | \(4.8758e{-}3\) | \(2.3682e{-}2\) | \(3.6564e{-}3\) | \(7.4153e{-}3\) |
\(\frac{1}{96}\) | 3 | \(1.1266\) e–1 | \(2.7333\) | \(4.8861e{-}3\) | \(2.3682e{-}2\) | \(3.6596e{-}3\) | \(7.4153e{-}3\) |
\(\frac{1}{96}\) | 4 | \(1.1186\) e–1 | \(2.6995\) e–1 | \(4.8874e{-}3\) | \(2.3682e{-}2\) | \(3.6598e{-}3\) | \(7.4153e{-}3\) |
\(\frac{1}{192}\) | \(*\) | \(7.5407e{-}3\) | \(4.7396e{-}2\) | \(2.9959e{-}3\) | \(2.0611e{-}2\) | \(1.8231e{-}3\) | \(4.2963e{-}3\) |
\(\frac{1}{192}\) | 1 | \(5.5060e{-}2\) | \(1.4802\) e–1 | \(2.9586e{-}3 \) | \(2.0194e{-}2\) | \(1.8251e{-}3\) | \(4.2712e{-}3\) |
\(\frac{1}{192}\) | 2 | \(5.4280e{-}2\) | \(1.4441\) e–1 | \(2.9635e{-}3\) | \(2.0194e{-}2\) | \(1.8259e{-}3\) | \(4.2712e{-}3 \) |
\(\frac{1}{192}\) | 3 | \(5.3930e{-}2\) | \(1.4334\) e–1 | \(2.9641e{-}3\) | \(2.0194e{-}2\) | \(1.8261e{-}3\) | \(4.2712e{-}3 \) |
\(\frac{1}{192}\) | 4 | \(5.3683e{-}2\) | \(1.4217\) e–1 | \(2.9641e{-}3\) | \(2.0194e{-}2\) | \(1.8261e{-}3\) | \(4.2712e{-}3\) |