Two-Step Hybrid Block Method for Solving Second Order Initial Value Problem of Ordinary Differential Equations

A. Ji̇moh
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Abstract

A new zero-stable two-step hybrid block method for solving second order initial value problems of ordinary differential equations directly is derived and proposed. In the derivation of the method, the assumed power series solution is interpolated at the initial and the hybrid points while its second ordered derivative is collocated at all the nodal and selected off-step points in the interval of consideration. The relevant properties of the method were examined and the method was found to be zero-stable, consistent and convergent. A comparison of the results by the method with the exact solutions and other results in literature shows that the method is accurate, simple and effective in solving the class of problems considered.
求解常微分方程二阶初值问题的两步混合分块法
推导并提出了一种直接求解常微分方程二阶初值问题的新型零稳定两步混合分块法。在该方法的推导过程中,假定的幂级数解在初始点和混合点处进行内插,而其二阶导数则在考虑区间内的所有节点点和选定的非步骤点处进行配置。对该方法的相关特性进行了研究,发现该方法具有零稳定性、一致性和收敛性。将该方法的结果与精确解以及文献中的其他结果进行比较后发现,该方法在解决所考虑的这一类问题时准确、简单且有效。
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