关键词: 两点边值问题;三次样条插值;高精度有限体积元方法;收敛性分析

Abstract:

A high accuracy finite volume element method was given based on cubic spline interpolation for linear and nonlinear twopoint boundary value problems of ordinary differential equations. The computational scheme(FVCS) was derived and the property of positive type was discussed. Further we presented the convergence analysis and the scheme was proved having fourth order error estimate in discrete energy norm. Finally, numerical examples including linear and nonlinear problems, and source term with singularity problem were given to illustrate the high efficiency and wide adaptation of the method.

Key words: twopoint boundary value problem; cubic spline interpolation; high accuracy finite volume element method; convergence analysis