Numerical Solution for Singular Boundary Value Problems Using a Pair of Hybrid Nyström Techniques

Abstract

This manuscript presents an efficient pair of hybrid Nyström techniques to solve second-order Lane–Emden singular boundary value problems directly. One of the proposed strategies uses three off-step points. The obtained formulas are paired with an appropriate set of formulas implemented for the first step to avoid singularity at the left end of the integration interval. The fundamental properties of the proposed scheme are analyzed. Some test problems, including chemical kinetics and physical model problems, are solved numerically to determine the efficiency and validity of the proposed approach.

Keywords

• hybrid block methods
• chemical kinetics and physical models
• Lane–Emden singular boundary value problems
• starting procedure
• convergence analysis