Numerical Integration with Exponential Fitting Factor for Singularly Perturbed Two Point Boundary Value Problems
K. Madhu Latha
Department of Mathematics, National Institute of Technology, Warangal, India.
K. Phaneendra *
Department of Mathematics, Kakatiya Institute of Technology & Science, Warangal, India.
Y. N. Reddy
Department of Mathematics, National Institute of Technology, Warangal, India.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we discuss the numerical integration with exponential fitting factor for singularly perturbed two-point boundary value problems. It is based on the fact that: the given SPTPBVP is replaced by an asymptotically equivalent delay differential equation. Then, numerical integration with exponential fitting factor is employed to obtain a tridiagonal system which is solved efficiently by Thomas algorithm. We discussed convergence analysis of the method. Model examples are solved and the numerical results are compared with exact solution.
Keywords: Singular perturbation problem, boundary layer, delay differential equation, fitting factor, trapezoidal rule