Title :
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
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;
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
DOI :
10.1109/ICCMS.2009.31
