Abstract Here we consider the second order Inhomogeneous Linear Initial Value Problems with constant coefficients. Two–step hybrid methods (i.e. of Numerov–type) are considered for addressing this problem. A special set of order conditions is given and solved for derivation a low cost new method. Actually, we manage to save one stage (function evaluation) per step for this type of problems in comparison with the best existed methods. This is crucial as demonstrated in various numerical tests where our new proposal outperforms standard methods in the relevant literature.

中文翻译：

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求解非齐次线性问题的显式九阶两步法 x″(t)=Λx(t)+f(t)

摘要 这里我们考虑具有常系数的二阶非齐次线性初值问题。两步混合方法（即Numerov 型）被考虑用于解决这个问题。给出并求解了一组特殊的阶条件，以推导出一种低成本的新方法。实际上，与现有的最佳方法相比，我们设法为此类问题的每一步节省了一个阶段（函数评估）。正如在各种数值测试中所证明的那样，这是至关重要的，我们的新提案优于相关文献中的标准方法。