Numerical solution of second-order singular problems arising in astrophysics by combining a pair of one-step hybrid block Nyström methods.

Abstract

[EN]A one-step hybrid block method which is applied for solving Lane-Emden second-order singular differential equations arising in astrophysics is developed. The present technique is obtained by considering three intra-step nodal points, which are chosen appropriately in order to get optimized errors of the main formulas approximating the solution and the first derivative at the final position of the block, and another approximation of the solution at an intermediate point. The stability properties and characteristics of the proposed strategy are analyzed. The new approach is combined with an appropriate algorithm which is applied to the first subinterval to circumvent the singular behaviour at the left endpoint of the integration interval. Some second-order singular differential problems are solved numerically to show the effectiveness and validity of the proposed technique, which has been compared with other strategies available in the recent literature. The presented results support the better performance of the developed scheme.