A New family of methods for solving delay differential equations

TL;DR

This paper introduces a new family of -methods for solving delay differential equations, combining decomposition techniques with implicit methods, and demonstrates their improved efficiency and stability over existing approaches.

Contribution

The paper develops a novel family of -methods using a combination of decomposition and implicit techniques, not previously explored for delay differential equations.

Findings

New methods are more efficient than existing ones.

Methods are stable and convergent.

Applications show improved performance.

Abstract

In the present paper, we introduce a new family of $ \theta-$methods for solving delay differential equations. New methods are developed using a combination of decomposition technique viz. new iterative method proposed by Daftardar Gejji and Jafari and existing implicit numerical methods. Using Butcher tableau, we observed that new methods are non Runge-Kutta methods. Further, convergence of new methods is investigated along with its stability analysis. Applications to variety of problems indicates that the proposed family of methods is more efficient than existing methods.