We prove that the two-step backward differentiation formula (BDF) method is stable on arbitrary time grids; while variable-step three-step scheme if almost all adjacent step ratios are less than 2.553. These results relax severe mesh restrictions in literature and provide a new understanding of BDF methods. Our main tools include discrete orthogonal convolution kernels an elliptic type matrix n...

Iterative methods which have high convergence order are crucial in computational mathematics since the iterates produce sequences converging to root of a non-linear equation. A plethora applications chemistry and physics require solution equations abstract spaces iteratively. The derivation iterative requires expansions using Taylor series formula higher-order derivatives not present method. Th...