Table 1 \(H=\frac{1}{6},\ h=\tau \)
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 | \(8.6118\) e−3 | \(2.6493\) e–2 | \(7.4344\) e−3 | \(1.5421\) e–2 |
\(\frac{1}{48}\) | 1 | \(4.0090\) e–2 | \(2.0819\) e–1 | \(8.5534e{-}3\) | \(2.5531\) e–2 | \(7.4495e{-}3\) | \(1.4833\) e–2 |
\(\frac{1}{48}\) | 2 | \(4.0086 \) e–2 | \(1.7485\) e–1 | \(8.6384e{-}3\) | \(2.5532\) e–2 | \(7.4785e{-}3\) | \(1.5375\) e–2 |
\(\frac{1}{48}\) | 3 | \(4.1043\) e–2 | \(1.7967\) e–1 | \(8.6403e{-}3\) | \(2.5532\) e–2 | \(7.4790e{-}3\) | \(1.5379\) e–2 |
\(\frac{1}{48}\) | 4 | \(4.1164\) e–2 | \(1.7947\) e–1 | \(8.6403e{-}3\) | \(2.5532 \) e–2 | \(7.4790e{-}3\) | \(1.5379 \) 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 | \(1.7513\) e–2 | \(1.0523\) e–1 | \(4.9351e{-}3\) | \(2.4967\) e–2 | \(3.6397e{-}3\) | \(7.3584e{-}3\) |
\(\frac{1}{96}\) | 2 | \(1.7951\) e–2 | \(9.1683\) e–2 | \(4.9457e{-}3\) | \(2.4967\) e–2 | \(3.6420e{-}3\) | \(7.4145e{-}3\) |
\(\frac{1}{96}\) | 3 | \(1.8186\) e–2 | \(9.3327\) e–2 | \(4.9458e{-}3\) | \(2.4967\) e–2 | \(3.6420e{-}3\) | \(7.4147 e{-}3\) |
\(\frac{1}{96}\) | 4 | \(1.8219\) e–2 | \(9.3540\) e–2 | \(4.9458e{-}3\) | \(2.4967 \) e–2 | \(3.6420e{-}3\) | \(7.4147e{-}3\) |
\(\frac{1}{192}\) | \(*\) | \( 7.5407e{-}3\) | \( 4.7396\) e–2 | \(2.9959e{-}3\) | \(2.0611\) e–2 | \(1.8231e{-}3\) | \(4.2963e{-}3\) |
\(\frac{1}{192}\) | 1 | \(7.9423e{-}3\) | \(5.1561\) e–2 | \(2.9899e{-}3\) | \(2.0539\) e–2 | \(1.8239e{-}3\) | \(4.2920e{-}3\) |
\(\frac{1}{192}\) | 2 | \(8.1633e{-}3\) | \(4.7424\) e–2 | \(2.9912e{-}3\) | \(2.0539\) e–2 | \(1.8240e{-}3\) | \(4.2920e{-}3\) |
\(\frac{1}{192}\) | 3 | \(8.1986e{-}3\) | \(4.7096\) e–2 | \(2.9912e{-}3\) | \(2.0539\) e–2 | \(1.8240e{-}3\) | \(4.2920e{-}3\) |
\(\frac{1}{192}\) | 4 | \(8.2016 e{-}3\) | \(4.7458\) e–2 | \(2.9912e{-}3\) | \( 2.0539\) e–2 | \(1.8240e{-}3\) | \(4.2920e{-}3\) |