基于三次B样条求解四阶线性边值问题  

The numerical solution of fourth order linear boundary value problems by using cubic B-splines

作　　者：李明珠[1,2] 丁效华[2] 王怡东[2] 

机构地区：[1]青岛理工大学理学院,青岛266033 [2]哈尔滨工业大学(威海)数学系,威海264209

出　　处：《黑龙江大学自然科学学报》2013年第6期711-715,共5页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(11271101);山东省自然科学基金青年项目(ZR2012AQ027)

摘　　要：利用三次B样条求解四阶线性微分方程边值问题的近似解。通过求解一个(n+3)维线性方程组,得到对应三次B样条函数的待定系数,进而得到边值问题的三次B样条近似解。利用本方法同时能够得到方程精确解的导数近似值,算法收敛且有二阶精度。数值算例说明了方法的有效性;与其他方法相比,本方法具有更高的精度。The numerical solution of linear fourth order boundary value problems is given by using cubic B-splines. The undetermined coefficients of cubic B-splines can be solved by an n ＋ 3 dimensional linear equations. The meth- od develops not only the cubic spline approximation solution but also the approximation derivatives of the analytic solution at the same time. This algorithm converges and has two-order accuracy. Finally, numerical examples are performed and comparisons with some other methods are also made. Numerical results show the algorithm has higher accuracy and efficiency.

关 键 词：三次B样条 边值问题 微分方程 线性方程组 

分 类 号：O241.8[理学—计算数学]