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Table 1 Maximum errors and the order of convergence of approximate solution 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