Numerical integration of third-order singular boundary-value problems of Emden–Fowler type using hybrid block techniques.

Abstract

[EN]In this article, a pair of hybrid block techniques is constructed and successfully applied to integrate Emden–Fowler third-order singular boundary problems. One of the proposed one-step hybrid block techniques is obtained by considering two intermediate points. The obtained method is then paired with a hybrid block strategy of order three to bypass the singularity at the left endpoint of the integration interval. Some third-order Emden–Fowler type problems are solved numerically to show the effectiveness of the proposed technique. The numerical results are compared with other recent numerical approaches in the literature, and the numerical simulations confirm the superiority and robust performance of the proposed strategy.