Hybrid Multistep Block Method for Solving Neutral Delay Differential Equations

The initial-value problem for first order single linear neutral delay differential equations (NDDEs) of constant and pantograph delay types have been solved by using hybrid multistep block method. The method has been derived by applying Thylor series interpolation polynomial and implementing the predictor-corrector formulas in PE(CE)(m) mode where m is the number of iterations for the proposed method. Both types of NDDEs will be solved at two-point simultaneously including the qff-step point with constant step-size. In order to, find the solution for NDDEs, the delay solutions of the unknown function will be interpolated using Lagrange interpolation polynomial and the derivative of the delay solutions will be obtained by applying divided difference formula. The order, consistency and convergence of the proposed method have been discussed in detail in the methods section. The properties of stability region for NDDEs have also been analysed. Numerical results presented have concluded that the proposed method is comparable with the existing method and is assumed to be reliable for solving first order NDDEs with constant and pantograph delay.