This paper discusses a direct three-point implicit block multistep method for direct solution of the general third-order initial value problems of ordinary differential equations using variable step size. The method is based on a pair of explicit and implicit of Adams type formulas which are implemented in PE(CE) t mode and in order to avoid calculating divided difference and integration coefficients all the coefficients are stored in the code. The method approximates the numerical solution at three equally spaced points simultaneously. The Gauss Seidel approach is used for the implementation of the proposed method. The local truncation error of the proposed scheme is studied. Numerical examples are given to illustrate the efficiency of the method.
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机译:本文讨论了一种直接三点隐式块多步法,该方法可以使用可变步长直接求解常微分方程的一般三阶初值问题。该方法基于在PE(CE) t 模式下实现的一对Adams型公式的显式和隐式,并且为了避免计算除差和积分系数,所有系数都存储在码。该方法同时在三个等距的点上近似数值解。高斯·赛德尔方法用于实施所提出的方法。研究了该方案的局部截断误差。数值例子说明了该方法的有效性。
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