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

作者：Lang Feng Gong^*; Xu Xiao Ping

来源：ScienceAsia, 2014, 40(6): 444-450.

DOI：10.2306/scienceasia1513-1874.2014.40.444

• numerical solution
• numerical derivative
• 4th-order two-point boundary value problem

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.

• 出版日期2014-12
• 单位中国海洋大学