半线性两点第三边值问题的紧有限体积方法  

Compact finite volume method for semi-linear two point boundary value problems of third kind

作　　者：董丽秀[1] 王同科[1] 

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《天津师范大学学报（自然科学版）》2015年第1期1-7,共7页Journal of Tianjin Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11471166)

摘　　要：研究半线性两点第三边值问题的高精度紧有限体积方法.在均匀网格剖分下,通过对方程的积分守恒形式使用多种离散技巧导出计算格式.该格式为一个非线性代数方程组,进一步给出了其Newton迭代解法.利用离散能量方法证明了在一定的正则性条件下,格式按照常见离散范数均具有四阶精度.数值算例验证了理论分析的正确性,说明格式可以高效地用于半线性两点第三边值问题的数值求解.A kind of high accuracy compact finite volume method is studied for semi-linear tWO point boundary value problem of third kind. The scheme is derived by discretizing the integral form of conservation law of the equation using some kinds of techniques under the assumption of uniform grid subdivision. The scheme is a system of nonlinear algebraic equations, which can be solved by Newton iterafive method. It is proved that the scheme has fourth order accuracy with respect to some kinds of discrete norms by using discrete energy method under the condition of certain regularity. A numerical example verifies the correctness of the theoretical analysis and shows that the scheme can be efficiently used to solve semi-linear two point bound- ary value problems of third kind.

关 键 词：两点边值问题 紧有限体积法 NEWTON迭代法 误差估计 

分 类 号：O241.82[理学—计算数学]