A proposed improved ratio method for the solution of IVPs in delay differential equations of various characteristics

This paper proposes an improved Ratio Method (IRM) to tackle Delay Differential Equations (DDEs) by employing a rational-type interpolating function. The Lagrange interpolation was used for approximating the delay argument. The consistency and convergence properties of IRM were analyzed. Moreover, the stability property of IRM using a test problem of DDE was investigated, and the corresponding region of stability was also obtained. The efficiency of IRM was demonstrated through illustrative examples of singularly perturbed and stiff DDEs. A comparative study of the results generated via IRM and that of the theoretical solution was presented.