Malaysian Journal of Mathematical Sciences, December 2020, Vol. 14(S)
Special Issue: 2nd International Conference on Applied & Industrial Mathematics and Statistics 2019 (ICoAIMS 2019)
Solving Neutral Delay Differential Equation of Pantograph Type
Ismail, N. I. N., Majid, Z. A., and Senu, N.
Corresponding Email: am_zana@upm.edu.my
Received date: 15 January 2020
Accepted date: 30 July 2020
Abstract:
Neutral Delay Differential Equation (NDDE) of pantograph type has been solved by developing a fifth order explicit multistep block method.
NDDE has become of great interest among researchers in its industrial applications. In finding the solution for the problem, a two-point explicit multistep block method has been modelled by applying Taylor Series interpolation polynomial. The proposed method will solve pantograph NDDE at two points concurrently with the strategy of consistent step-size. The implementation is based on multistep method Adam Bashforth formula in predictor mode. In handling pantograph delay, Lagrange interpolation polynomial needs to be applied to find the solution of delay terms that are larger than the initial value given. The delay derivatives are estimated using divided difference formula. The order and convergence have been determined to ensure the reliability of the proposed explicit block method. The stability analysis has been constructed using test equation for NDDE. Numerical results obtained have shown that the suggested method is suitable and applicable for solving pantograph equation.
Keywords: Explicit Multistep Block Method, Initial-value problem, Neutral Delay Differential Equation, Pantograph delay
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