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Variable Step-Size Control Based on Two-Steps for Radau IIA Methods

机译:基于Radau IIA方法的两步的可变梯级控制

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Two-step embedded methods of order s based on s-stage Radau IIA formulas are considered for the variable step-size integration of stiff differential equations. These embedded methods are aimed at local error control and are computed through a linear combination of the internal stages of the underlying method in the last two steps. Particular embedded methods for 2 = s = 7 internal stages with good stability properties and damping for the stiff components are constructed. Furthermore, a new formula for step-size change is proposed, having the advantage that it can be applied to any s-stage Radau IIA method. It is shown through numerical testing on some representative stiff problems that the RADAU5 code by Hairer and Wanner with the new strategy performs as well or even better as with the standard one, which is only feasible for an odd number of stages. Numerical experiments support the efficiency and flexibility of the new step-size change strategy.
机译:基于S阶段Radau IIA公式的两步嵌入方法S是刚性微分方程的可变步长集成的。这些嵌入方法旨在局部错误控制,并通过底层方法的内部阶段的线性组合在最后两个步骤中计算。构造了2 <= S <= 7个内级的特定嵌入方法,具有良好的稳定性,并且用于硬质部件的阻尼。此外,提出了一种用于阶梯尺寸变化的新公式,其优点是它可以应用于任何S-阶段的Radau IIA方法。通过数值测试显示一些代表性僵硬问题,即毛发和WANNER与新策略的RADAU5代表和WANNER一起表现,也可以与标准的策略一样更好,这对于奇数阶段仅可行。数值实验支持新的阶梯大小的变化策略的效率和灵活性。

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