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

Abstract

Summary.We shall consider an application of simple exponential splines to the numerical solution of singular perturbation problem. The computational effort involved in our collocation method is less than that required for the other methods of exponential type.

Numerical solutions of the reaction diffusion system by using exponential cubic B-spline collocation algorithms

“…Academic articles have dealt with the numerical solutions of the di erential equations using the exponential B-splines. The exponential Bsplines are used with the collocation method to nd the numerical solution of the singular perturbation problem by Manabu Sakai and his colleague [3]. Another application of the collocation method using the cardinal exponential B-splines was shown for nding the numerical solutions of the singularly perturbed boundary problem in the study of Desanka Radunuvic [4].…”

Multiresolution exponential B-splines and singularly perturbed boundary problem

“…To calculate parameters of a fitted finite difference operator, Sakai and Usmani [18] use the collocation method based on the third order exponential B-spline basis. As they use a uniform mesh, multiresolution properties of basis functions are not utilized.…”

“…In this paper we consider whether two approaches in construction of ε-uniform methods, suitable for solving such problems, can be combined by use of exponential splines. We analyze in more details some properties of the exponential B-splines used in [18], and derive recursions needed for a multiresolution approach. We fit an operator by approximating a solution on an exponential spline basis, and fit a mesh by use of multiresolution.…”

Exponential B-splines and the partition of unity property

“…In approximation theory exponential splines are modeling data that exhibits sudden growth or decay and for which polynomials are illsuited because of their oscillatory behavior. Some of the mathematical issues regarding exponential splines in the theory of interpolation and approximation can be found in the, albeit incomplete, list of references [1,5,6,13,[16][17][18][19][20].…”