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Research articles

ScienceAsia 40 (2014): 444-450 |doi: 10.2306/scienceasia1513-1874.2014.40.444

A new cubic B-spline method for approximating the solution of a class of nonlinear second-order boundary value problem with two dependent variables

Feng-Gong Lang*, Xiao-Ping Xu

ABSTRACT:     In this paper, we will apply cubic B-splines on a uniform mesh to explore the numerical solutions and numerical derivatives of a class of nonlinear second-order boundary value problems with two dependent variables. Our new method is based on the cubic spline interpolation. The analytical solutions and any-order derivatives can be well approximated with 4th order accuracy. Furthermore, our new method is also able to solve general nonlinear 4th-order two-point boundary value problems. Numerical results show that our method is very practical and effective.

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School of Mathematical Sciences, Ocean University of China, Qingdao, Shandong, 266100, China

* Corresponding author, E-mail: fenggonglang@sina.com

Received 26 May 2013, Accepted 16 Feb 2014