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HIGH-ORDER NUMERICAL METHOD FOR TWO-POINT BOUNDARY VALUE PROBLEMS

机译：两点边值问题的高阶数值方法

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In this paper the two-point boundary value problem is transformed into general first-order ordinary differential equation system through introduction of conditions of an integral character to supplement the simultaneous set of first-order equations. A new discrete approximation of a high-order compact difference scheme is presented for the first-order system. It is a block-bidiagonal profile and removes the limits of other high-order discrete schemes at the interval ends. The numerical tests of a seventh-order compact difference scheme show that the proposed scheme is very convenient and efficient for linear and nonlinear two-point boundary value problems. (C) 1995 Academic Press, Inc. [References: 6]
机译：通过引入积分性质的条件来补充一阶方程组的同时性，将两点边值问题转化为一般的一阶常微分方程组。针对一阶系统，提出了一种新的高阶紧致差分方案的离散逼近。它是一个块双角轮廓，并且消除了其他高阶离散方案在区间末端的限制。七阶紧致差分方案的数值试验表明，该方案对于线性和非线性两点边值问题非常方便和有效。 （C）1995 Academic Press，Inc. [参考：6]

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