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.
Share and Cite
ISRP Style
Normah Maan, Aminu Barde, Analytical technique for neutral delay differential equations with proportional and constant delays, Journal of Mathematics and Computer Science, 20 (2020), no. 4, 334--348
AMA Style
Maan Normah, Barde Aminu, Analytical technique for neutral delay differential equations with proportional and constant delays. J Math Comput SCI-JM. (2020); 20(4):334--348
Chicago/Turabian Style
Maan, Normah, Barde, Aminu. "Analytical technique for neutral delay differential equations with proportional and constant delays." Journal of Mathematics and Computer Science, 20, no. 4 (2020): 334--348
Keywords
- Neutral delay differential equations
- He's polynomial
- natural transform method
- homotopy analysis method
MSC
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