# A second order convergent initial value method for singularly perturbed system of differential-difference equations of convection diffusion type

Volume 25, Issue 1, pp 73--83
Publication Date: May 09, 2021 Submission Date: February 23, 2021 Revision Date: March 30, 2021 Accteptance Date: April 07, 2021
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### Authors

L. S. Senthilkumar - Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and technology, Kattankulathur-603 203, Tamilnadu, India. R. Mahendran - Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and technology, Kattankulathur-603 203, Tamilnadu, India. V. Subburayan - Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and technology, Kattankulathur-603 203, Tamilnadu, India.

### Abstract

In this article, a system of second order singularly perturbed delay differential equations of convection diffusion type problem is considered. An asymptotic expansion approximation of the solution is constructed. Further the asymptotic expansion approximation is numerically approximated using the Runge Kutta methods and hybrid finite difference methods. The error estimate is obtained and it is of almost second order. Numerical examples are given to illustrate the present method.

### Share and Cite

##### ISRP Style

L. S. Senthilkumar, R. Mahendran, V. Subburayan, A second order convergent initial value method for singularly perturbed system of differential-difference equations of convection diffusion type, Journal of Mathematics and Computer Science, 25 (2022), no. 1, 73--83

##### AMA Style

Senthilkumar L. S., Mahendran R., Subburayan V., A second order convergent initial value method for singularly perturbed system of differential-difference equations of convection diffusion type. J Math Comput SCI-JM. (2022); 25(1):73--83

##### Chicago/Turabian Style

Senthilkumar, L. S., Mahendran, R., Subburayan, V.. "A second order convergent initial value method for singularly perturbed system of differential-difference equations of convection diffusion type." Journal of Mathematics and Computer Science, 25, no. 1 (2022): 73--83

### Keywords

• Delay differential equations
• singularly perturbed problem
• asymptotic expansion approximation
• initial value method
• Shishkin mesh

•  34K10
•  34K26
•  34K28

### References

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