Dahlquist, G. (1959) Convergence and Stability in the Numerical Integration of Ordinary Differential Equation. Mathematics Scandinavia, 4, 33-53.
https://doi.org/10.7146/math.scand.a-10454

has been cited by the following article:

• TITLE: An Eight Order Two-Step Taylor Series Algorithm for the Numerical Solutions of Initial Value Problems of Second Order Ordinary Differential Equations

  AUTHORS: Ayodele Olakiitan Owolanke, Ohi Uwaheren, Friday Oghenerukevwe Obarhua

  KEYWORDS: Power Series, Collocation and Taylor’s Series Algorithm

  JOURNAL NAME: Open Access Library Journal, Vol.4 No.6, June 19, 2017

  ABSTRACT: Our focus is the development and implementation of a new two-step hybrid method for the direct solution of general second order ordinary differential equation. Power series is adopted as the basis function in the development of the method and the arising differential system of equations is collocated at all grid and off-grid points. The resulting equation is interpolated at selected points. We then analyzed the resulting scheme for its basic properties. Numerical examples were taken to illustrate the efficiency of the method. The results obtained converge closely with the exact solutions.