A Novel Numerical Scheme for the Solution of a System of First-Order Delay Differential Equations - Uncu, Sevket; Cimen, Erkan (Communications in Mathematics and Applications, 2026)
In this paper, an efficient finite difference approach is introduced to solve the system of first-order delay differential equations. The method used for this approach is based on integral identities for the quadrature formula with integral term remainder terms, and using this method a novel difference scheme is constructed. Then, first-order convergence for the method in the discrete maximum norm is proved. Finally, a test problem is presented that is solved using both the proposed and classical Euler methods, which support the theoretical findings. Considering these results, this scheme has greater efficiency and accuracy than the classical Euler scheme, although it has the same convergence rate. So, these results show that the proposed method is reliable, efficient and accurate.