A new two-step modified explicit hybrid method with parameters depending on the step-size is constructed. This method is derived using the coefficients from a sixth-order explicit hybrid method with extended interval of absolute stability and then imposed each stage of the modified formula to exactly integrate the differential equations with solutions that can be expressed as linear combinations of and , where is the known frequency. Numerical results show the advantage of the new method for solving oscillatory problems.

中文翻译：

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具有步长相关参数的振动问题两步修正显式混合方法

构造了一种新的两步修正显式混合方法，其参数取决于步长。本方法采用的系数从与绝对稳定扩展的间隔六阶显式混合方法的修正公式的每个阶段衍生的，然后施加到恰好集成的解决方案的微分方程，可以被表示为的线性组合和，其中是已知频率。数值结果表明，该方法可以解决振动问题。