Direct Multistep Method for Solving Retarded and Neutral Delay Differential Equation with Boundary and Initial Value Problems

The boundary and initial conditions that are related to the retarded and neutral delay differential equations, respectively, will be resolved in this work by using the previous direct multistep method. This method solves retarded and neutral delay differential equations directly by implementing the proposed method without converting it to a first-order system. For boundary value problems, the shooting strategy incorporated with the Newton method is utilized to predict the guessing value. The initial value problem for neutral delay differential equations on the other hand is resolved directly with special attention to the differential part of the problem. Several numerical examples are investigated to observe the capability of the developed strategies and methods for solving retarded delay differential equations with boundary value problems and neutral delay differential equations with initial value problems.