iosr-Jm   Volume-1 ~ Issue-2

ABSTRACT: In this paper, we propose numerical method to solve singularly perturbed delay differential
equations which works smoothly in both the cases, i.e., whether the delay is of O( ) or of o( ) . The numerical
method uses the modified upwind finite difference scheme on a special type of mesh to tackle the delay
argument. The stability and error analysis is given for in both the cases, when the sign of the coefficient of the
reaction term is negative or positive. To demonstrate the efficiency of the method and how to discuss the size of
the delay argument affects the layer behaviour we have implemented it on several test examples.
Keywords: Boundary Layer modified upwind finite difference scheme, Singular perturbation delay differential
equation.

[1] R. Bellman, K. L. Cooke, Differential-Difference Equations, Academic Press, New York, USA, 1963.
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arising in optical control theory, J. Optim. Theory Appl. 106 (2000) 309-335.
[4] M. K. Kadalbajoo, K. K. Sharma, Numerical analysis of singularly perturbed delay differential equations with layer behavior,
Applied Mathematics and Computation, 157 (2004) 11–28.
[5] M. K. Kadalbajoo, K. K. Sharma, Numerical treatment of boundary value problems for second order singularly perturbed delay
differential equations, Computational & Applied Mathematics, 24 (2005) 151–172.
[6] M. K. Kadalbajoo, K. K. Sharma, A Numerical method based on finite differences for boundary value problems for singularly
perturbed delay differential equations, Applied Mathematics & Computation, 197 (2008) 692–707.
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[1] Chlodovsky, I (1937). Sur le development des fonctions definies dans un interval infini en series de polynomes de M S Bernstein composition math, 4,380-93 .
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Abstract: Calendar is the key of our life. In every aspect of our life we need to follow it. It is not possible to keep calendar of the range ZERO to INFINITE. Generally we can have calendar up-to 300 years from the current one. There is some formula to calculate the year/month etc. but they have some limitation, they cannot be applicable for ZERO to INFINITE calendar. In this paper, we proposed a novel methodology to extract the day, month, year from ZERO to INFINITE range of calendar with a few seconds.
Keywords: Mid-point of the Operator, leap – year.

[1] www.scribd.com/.../11707676-An-Exploratory-Study-of-Personal-Calendar-Use.
[2] iris.usc.edu/information/Iris-Conferences.html.
[3] www.cs.utep.edu/novick/courses/CS5317/Schedule.pdf.

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