Ken, Yap Lee; Ismail, Fudziah; Suleiman, Mohamed; Amin, Suriah Md. Block methods based on Newton interpolations for solving special second order ordinary differential equations directly. (English) Zbl 1186.65088 J. Math. Stat. 4, No. 3, 174-180 (2008). Summary: We are focused mainly on the derivation of 2 and 3-point block methods with constant coefficients for solving special second order ordinary differential equations directly based on the Newton-Gregory backward interpolation formula. The performance of the new methods was compared with the conventional 1-point method using a standard set of test problems. Numerical results are presented to illustrate the effectiveness of the methods in terms of the total number of steps taken, maximum error and execution time. The results suggest a significant improvement in efficiency of the r-point block method. Cited in 3 Documents MSC: 65L05 Numerical methods for initial value problems involving ordinary differential equations Keywords:initial value problems; special second order oridnary differential equations; block method; error bounds; Newton-Gregory backward interpolation formula; performance; numerical results; effectiveness PDFBibTeX XMLCite \textit{Y. L. Ken} et al., J. Math. Stat. 4, No. 3, 174--180 (2008; Zbl 1186.65088)