Theory and Modern Applications
Table 2 Maximum errors and the order of convergence of approximate solution ṽ with respect to τ for Example 1
From: Implicit methods for the first derivative of the solution to heat equation
(\(h=2^{-\mu }\), \(\tau =2^{-\lambda } \)) | (\(h=2^{-\mu }\), \(\tau =2^{-(\lambda +1)} \)) | \(\Vert \varepsilon _{v}^{2^{-\mu },2^{-\lambda }} \Vert \) | \(\Vert \varepsilon _{v}^{2^{-\mu },2^{- ( \lambda +1 ) }} \Vert \) | \(\Re _{v}^{\tau }\) |
|---|---|---|---|---|
(2−9,2−6) | (2−9,2−7) | 6.087E − 2 | 3.058E − 2 | 1.991 |
(2−9,2−7) | (2−9,2−8) | 3.058E − 2 | 1.531E − 2 | 1.997 |
(2−9,2−8) | (2−9,2−9) | 1.531E − 2 | 7.634E − 3 | 2.006 |
(2−9,2−9) | (2−9,2−10) | 7.634E − 3 | 3.791E − 3 | 2.014 |
(2−9,2−10) | (2−9,2−11) | 3.791E − 3 | 1.867E − 3 | 2.031 |