Adam’s type block methods for solving neutral delay differential equation with constant and panthograph delay

The numerical solutions for Neutral Delay Differential Equation (NDDE) have been studied in this thesis. Two numerical methods which are known as an explicit multi- step block method and a hybrid multistep block method have been introduced. The multistep block methods will be implemented in solving NDDE with constant and pantograph delay types using constant step size. Both methods have been derived by using Taylor series polynomial where the implementations of the methods are based on predictor-corrector formulas. In this research, the source codes for the numerical solutions were written in C language. In the developed algorithm, the delay terms have been approximated by using divided difference formulas depending on the ap- plicability of both methods in every iteration. Both constant and pantograph delay types have their own uniqueness in finding the solutions of the delay terms. The order, consistency and zero-stability for the block methods have been determined to ensure their applicability in solving both types of NDDE. The convergence and sta- bility analysis have also been analyzed. The stability polynomials for both multistep block methods have been obtained and their stability regions have been discussed. In conclusion, the numerical results obtained have proven that the proposed block methods give accurate results in terms of maximum and average error. The block methods have also produced less computational time in solving NDDE with con- stant and pantograph delay types.

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