Analysis of new RET single-step method for solving stiff and singular types of ordinary differential equations

This study introduces a novel single-step approach that employs an interpolation technique combining a rational function based on a polynomial with a trigonometric interpolation component (RET) for addressing stiff and singular ordinary differential equations (ODEs). The characteristics of the proposed method—such as consistency, convergence, zero stability, and order of accuracy—are thoroughly investigated. To assess its effectiveness, the RET scheme is applied to three distinct numerical problems, and the computed results are evaluated against the corresponding analytical solutions. The findings indicate that RET offers a reliable, precise, and efficient means for numerically solving both stiff and singular ODEs