Spline techniques for the numerical solution of singular perturbation problems

Authors:
M. K. Kadalbajoo;K. C. Patidar
Affiliations:
Professor, Department of Mathematics, Indian Institute of Technology, Kanpur, India;Research Scholar, Department of Mathematics, Indian Institute of Technology, Kanpur, India
Venue:
Journal of Optimization Theory and Applications
Year:
2002

Citing 2
Cited 2

A finite element method for a singularly perturbed boundary value problem

Numerische Mathematik
A class of simple exponential B-splines and their application to numerical solution to singular perturbation problems

Numerische Mathematik

A recent survey on computational techniques for solving singularly perturbed boundary value problems

International Journal of Computer Mathematics
Variable mesh spline approximation method for solving singularly perturbed turning point problems having interior layer

Neural, Parallel & Scientific Computations

Quantified Score

Hi-index	0.00

Visualization

Abstract

One-dimensional singularly-perturbed two-point boundary-value problems arising in various fields of science and engineering (for instance, fluid mechanics, quantum mechanics, optimal control, chemical reactor theory, aerodynamics, reaction-diffusion processes, geophysics, etc.) are treated. Either these problems exhibits boundary layer(s) at one or both ends of the underlying interval or they possess oscillatory behavior depending on the nature of the coefficient of the first derivative term. Some spline difference schemes are derived for these problems using splines in compression and splines in tension. Second-order uniform convergence is achieved for both kind of schemes. By making use of the continuity of the first-order derivative of the spline function, a tridiagonal system is obtained which can be solved efficiently by well-known algorithms. Numerical examples are given to illustrate the theory.