中文摘要：

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.

英文摘要：

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.