TY - JOUR
T1 - One-Step Hybrid Block Method Containing Third Derivatives and Improving Strategies for Solving Bratu's and Troesch's  Problems
AU - Ajani Rufai , Mufutau
AU - Ramos , Higinio
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 946
EP - 972
PY - 2020
DA - 2020/06
SN - 13
DO - http://doi.org/10.4208/nmtma.OA-2019-0157
UR - https://global-sci.org/intro/article_detail/nmtma/16961.html
KW - Ordinary differential equations, Bratu's problem, Troesch's problem, boundary
value problems, hybrid block method, homotopy-type strategy.
AB - <p style="text-align: justify;">In this paper, we develop a one-step hybrid block method for solving
boundary value problems, which is applied to the classical one-dimensional Bratu&#39;s
and Troesch&#39;s problems. The convergence analysis of the new technique is discussed, and some improving strategies are considered to get better performance
of the method. The proposed approach produces discrete approximations at the grid
points, obtained after solving an algebraic system of equations. The solution of this
system is obtained through a homotopy-type strategy used to provide the starting
points needed by Newton&#39;s method. Some numerical experiments are presented to
show the performance and effectiveness of the proposed approach in comparison
with other methods that appeared in the literature.</p>