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Table 3 Maximum errors and the order of convergence of approximate solution 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