**InternationaleJournals**

Numerical Integration Of General Singular Perturbation Problems- Technique 2

**Loka Pavani ^{a}
and Y.N Reddy^{ b} **

** ^{a}**
Department of mathematics, Chaitanya Bharathi Institute of Technology, Hyderabad, 500 075, India.

^{b
}Department of mathematics, National Institute of Technology, Warangal, 506 004, India.

**Abstract**

In this paper, a numerical integration method is presented for solving general singularly perturbed two-point boundary value problems. This method does not depend on asymptotic expansions. The main feature of this method is that it does not require a very fine mesh size. The original second order differential equation is replaced by an approximate first-order differential equation called ‘neutral type’ equation with a small deviating argument. Simpsons 1/3 rule is used to obtain a three term recurrence relation. Thomas Algorithm is used to solve the resulting tridiagonal algebraic system of equations. The proposed method is iterative on the deviating argument. The method is to be repeated for different choices of the deviating argument. Two linear and one non-linear examples with left-end boundary layer, one example each for right end boundary layer, internal layer and two layers are solved and the computational results are presented. It is observed that the present method approximates the exact solution very well.

**Keywords:** Singular perturbation problems, boundary
layer, neutral type equations, deviating argument, Thomas Algorithm.

**International
eJournal of Mathematical Sciences, Technology and Humanities**

**Volume** 1,
**Issue** 2, **Pages**: 153 - 173