A Difference Scheme Based on Spline Approximations to Solve the Singularly-perturbed Neumann Problems

Author

Liu, Huan-Wen ; Liu, Li-Bin

Author_Institution

Fac. of Math. & Comput. Sci., Guangxi Univ. for Nat., Nanning

fYear

2009

fDate

20-22 Feb. 2009

Firstpage

209

Lastpage

212

Abstract

In this paper, a difference scheme based on the quartic splines for solving the singularly-perturbed two-point boundary-value problem of second-order ordinary differential equations subject to Neumann-type boundary conditions are derived. The accuracy order of the schemes is O(h⁴) not only at the interior nodal points but also at the two endpoints, which are better than general center finite difference method. Finally, the numerical results are given to illustrate the efficiency of our methods.

Keywords

algebra; approximation theory; boundary-value problems; finite difference methods; singularly perturbed systems; splines (mathematics); Neumann-tpye boundary conditions; boundary-value problem; finite difference method; quar- tic splines; second-order ordinary differential equations; singularly-perturbed Neumann problems; spline approximations; Boundary conditions; Boundary value problems; Computational modeling; Finite difference methods; Finite wordlength effects; Hydrogen; Interpolation; Mathematical model; Mathematics; Spline; Neumann condition; difference scheme; singularly-perturbed problem; spline approximation;

fLanguage

English

Publisher

ieee

Conference_Titel

Computer Modeling and Simulation, 2009. ICCMS '09. International Conference on

Conference_Location

Macau

Print_ISBN

978-0-7695-3562-3

Electronic_ISBN

978-1-4244-3561-6

Type

conf

DOI

10.1109/ICCMS.2009.31

Filename

4797384