Analytical technique for neutral delay differential equations with proportional and constant delays

Volume 20, Issue 4, pp 334--348 http://dx.doi.org/10.22436/jmcs.020.04.07

Publication Date: March 06, 2020 Submission Date: December 17, 2019 Revision Date: January 04, 2020 Accteptance Date: January 16, 2020

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Authors

Normah Maan - Department of Mathematical Sciences, Universiti Teknologi, 81310 Skudai, Johor, Malaysia. Aminu Barde - Department of Mathematical Sciences, Universiti Teknologi, 81310 Skudai, Johor, Malaysia. - Department of Mathematical Sciences, Abubakar Tafawa Balewa University, Bauchi, Nigeria.

Abstract

Neutral delay differential equations (NDDEs) are a type of delay differential equations (DDEs) that arise in numerous areas of applied sciences and play a vital role in mathematical modelling of real-life phenomena. Some techniques have experienced difficulties in finding the approximate analytical solution which converges rapidly to the exact solution of these equations. In this paper, an analytical approach is proposed for solving linear and nonlinear NDDEs with proportional and constant delays based on the homotopy analysis method (HAM) and natural transform method where the nonlinear terms are simply calculated as a series of, He's polynomial. The proposed method produces solutions in the form of a rapidly convergent series which leads to the exact solution from only a few numbers of iterations. Some illustrative examples are solved, and the convergence analysis of the proposed techniques was also provided. The obtained results reveal that the approach is very effective and efficient in handling both linear and nonlinear NDDEs with proportional and constant delays and can also be used in various types of linear and nonlinear problems.

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Keywords

• Neutral delay differential equations
• He's polynomial
• natural transform method
• homotopy analysis method

MSC

•  65L03
•  34K99

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