Table 2 Maximal differences between successive approximations ${\mathit{u}}^{\mathbf{(}\mathit{k}\mathbf{)}}$ by Newton’s method ( 4.1 ) with ${\mathit{D}}_{\mathbf{1}}\mathbf{=}\mathbf{1}$ , ${\mathit{D}}_{\mathbf{2}}\mathbf{=}\mathbf{0.5}$ , ${\mathit{D}}_{\mathbf{3}}\mathbf{=}\mathbf{0.2}$ , $\mathit{h}\mathbf{=}\mathbf{0.01}$ , ${\mathit{h}}_{\mathbf{0}}\mathbf{=}\mathbf{0.01}$

t

$\mathbf{|}{\mathit{u}}^{\mathbf{(}\mathbf{1}\mathbf{)}}\mathbf{-}{\mathit{u}}^{\mathbf{(}\mathbf{0}\mathbf{)}}\mathbf{|}$

$\mathbf{|}{\mathit{u}}^{\mathbf{(}\mathbf{2}\mathbf{)}}\mathbf{-}{\mathit{u}}^{\mathbf{(}\mathbf{1}\mathbf{)}}\mathbf{|}$

$\mathbf{|}{\mathit{u}}^{\mathbf{(}\mathbf{3}\mathbf{)}}\mathbf{-}{\mathit{u}}^{\mathbf{(}\mathbf{2}\mathbf{)}}\mathbf{|}$

$\mathbf{|}{\mathit{u}}^{\mathbf{(}\mathbf{4}\mathbf{)}}\mathbf{-}{\mathit{u}}^{\mathbf{(}\mathbf{3}\mathbf{)}}\mathbf{|}$

$\mathbf{|}{\mathit{u}}^{\mathbf{(}\mathbf{5}\mathbf{)}}\mathbf{-}{\mathit{u}}^{\mathbf{(}\mathbf{4}\mathbf{)}}\mathbf{|}$