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.

翻译：在本文件中,我们引入了一个新的体系,即用于解决延迟差分方程的元-元方法;在开发新方法时结合了分解技术,即Daftardar Gejji和Jafari提出的新的迭代方法以及现有的隐含数字方法;在使用布彻表au时,我们发现新方法是非龙格-库塔方法;此外,对新方法的趋同及其稳定性分析进行了调查;对各种问题的应用表明,拟议方法的组合比现有方法更有效。