Theory and Modern Applications
Table 3 Maximum errors and the order of convergence of approximate solution ṽ with respect to h and τ for Example 2
From: Implicit methods for the first derivative of the solution to heat equation
(\(h=2^{-\mu }\), \(\tau =2^{-\lambda}\)) | (\(h=2^{-(\mu +1)}\), \(\tau =2^{-(\lambda +1)}\)) | \(\Vert \varepsilon _{v}^{2^{-\mu },2^{-\lambda }} \Vert \) | \(\Vert \varepsilon _{v}^{2^{- ( \mu +1 ) },2^{- ( \lambda+1 ) }} \Vert \) | \(\widetilde{\Re }_{v}^{h,\tau }\) |
|---|---|---|---|---|
(2−4,2−13) | (2−5,2−14) | 1.0567E − 2 | 3.1449E − 3 | 3.360 |
(2−5,2−14) | (2−6,2−15) | 3.1449E − 3 | 8.5353E − 4 | 3.685 |
(2−6,2−15) | (2−7,2−16) | 8.5353E − 4 | 2.2209E − 4 | 3.843 |
(2−7,2−16) | (2−8,2−17) | 2.2209E − 4 | 5.6628E − 5 | 3.922 |