Table 2 \(H=\frac{1}{12},\ h=\tau \)
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 | \( 8.4704\) e–2 | \(2.2515\) e–1 | \(8.7074e{-}3\) | \(2.4202\) e–2 | \(7.5866e{-}3\) | \(1.6164\) e–2 |
\(\frac{1}{48}\) | 2 | \(8.0447\) e–2 | \(1.9139\) e–1 | \(8.7352e{-}3\) | \(2.4202\) e–2 | \(7.5212e{-}3\) | \(1.5371\) e–2 |
\(\frac{1}{48}\) | 3 | \(7.9085\) e–2 | \(1.8885\) e–1 | \(8.7459e{-}3\) | \(2.4202\) e–2 | \(7.5203e{-}3\) | \(1.5388\) e–2 |
\(\frac{1}{48}\) | 4 | \(7.7713\) e–2 | \(1.8467\) e–1 | \(8.7464e{-}3\) | \(2.4202\) e–2 | \(7.5202e{-}3\) | \(1.5389\) e–2 |
\(\frac{1}{96}\) | \(*\) | \(1.4800\) e–2 | \(9.5488\) e–2 | \(4.9541e{-}3\) | \(2.5220\) e–2 | \(3.6348e{-}3\) | \( 7.4154e{-}3\) |
\(\frac{1}{96}\) | 1 | \(3.7063\) e–2 | \(1.0595\) e–1 | \(4.9336e{-}3\) | \(2.4609\) e–2 | \(3.6506e{-}3\) | \(7.4109e{-}3\) |
\(\frac{1}{96}\) | 2 | \(3.5576\) e–2 | \(8.4116\) e–2 | \(4.9480e{-}3\) | \(2.4609\) e–2 | \(3.6484e{-}3\) | \(7.4152e{-}3\) |
\(\frac{1}{96}\) | 3 | \(3.5206\) e–2 | \(8.2344\) e–2 | \(4.9480e{-}3\) | \(2.4609 \) e–2 | \(3.6481e{-}3\) | \(7.4153e{-}3\) |
\(\frac{1}{96}\) | 4 | \(3.4930\) e–2 | \(8.0713\) e–2 | \(4.9480e{-}3\) | \(2.4609 \) e–2 | \(3.6481e{-}3\) | \(7.4153e{-}3\) |
\(\frac{1}{192}\) | \(*\) | \(7.5407e{-}3\) | \(4.7396\) e–2 | \(2.9959e{-}3\) | \(2.0611\) e–2 | \(1.8231e{-}3\) | \(4.2963e{-}3\) |
\(\frac{1}{192}\) | 1 | \(1.3608\) e–2 | \(5.2234\) e–2 | \(2.9850e{-}3\) | \(2.0431\) e–2 | \(1.8251e{-}3\) | \(4.2847e{-}3\) |
\(\frac{1}{192}\) | 2 | \(1.3257\) e–2 | \(4.1956\) e–2 | \(2.9875e{-}3\) | \(2.0431\) e–2 | \(1.8249e{-}3\) | \(4.2847e{-}3\) |
\(\frac{1}{192}\) | 3 | \(1.3210\) e–2 | \(4.2262\) e–2 | \(2.9875e{-}3\) | \(2.0431\) e–2 | \(1.8249e{-}3\) | \(4.2847e{-}3\) |
\(\frac{1}{192}\) | 4 | \(1.3183 \) e–2 | \(4.2067\) e–2 | \(2.9875e{-}3\) | \(2.0431\) e–2 | \(1.8249e{-}3\) | \(4.2847e{-}3\) |