TY - JOUR
T1 - An Optimized Two-Step Hybrid Block Method Formulated in Variable Step-Size Mode for Integrating $y''=f(x,y,y')$ Numerically
AU - Gurjinder Singh & Higinio Ramos
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 640
EP - 660
PY - 2018
DA - 2018/12
SN - 12
DO - http://doi.org/10.4208/nmtma.OA-2018-0036
UR - https://global-sci.org/intro/article_detail/nmtma/12913.html
KW - 
AB - <p style="text-align: justify;">An optimized two-step hybrid block method is presented for integrating general second order initial value problems numerically. The method considers two intra-step points which are selected adequately in order to optimize the local truncation errors of the main formulas for the solution and the first derivative at the final point of the block. The new proposed method is consistent, zero-stable and has seventh algebraic order of convergence. To illustrate the performance of the method, some numerical experiments are presented for solving this kind of problems, in comparison with methods of similar characteristics in the literature.</p>