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Table 2 Maximum errors and the order of convergence of approximate solution 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