Theory and Modern Applications
Table 1 Maximum errors and the order of convergence of approximate solution ṽ with respect to h and τ for Example 1
From: Implicit methods for the first derivative of the solution to heat equation
(\(h=2^{-\mu }\), \(\tau =2^{-\lambda }\)) | (\(h=2^{-(\mu +1)}\), \(\tau =2^{- ( \lambda +2 ) }\)) | \(\Vert \varepsilon _{v}^{2^{-\mu },2^{-\lambda }} \Vert \) | \(\Vert \varepsilon _{v}^{2^{- ( \mu +1 ) },2^{- ( \lambda+2 ) }} \Vert \) | \(\Re _{v}^{h,r}\) |
|---|---|---|---|---|
(2−5,2−12) | (2−6,2−14) | 2.438E − 2 | 6.383E − 3 | 3.820 |
(2−6,2−14) | (2−7,2−16) | 6.383E − 3 | 1.633E − 3 | 3.909 |
(2−5,2−13) | (2−6,2−15) | 2.439E − 2 | 6.385E − 3 | 3.820 |
(2−6,2−15) | (2−7,2−17) | 6.385E − 3 | 1.633E − 3 | 3.910 |