论文标题
通用的显式伪两个步长runge-kutta-nyström方法，用于解决二阶初始值问题
Generalized explicit pseudo two-step Runge-Kutta-Nyström methods for solving second-order initial value problems
论文作者
论文摘要
一类显式伪两步runge-kutta-nyström（geptrkn）方法用于求解二阶初始值问题$ y'''= f（t，y，y，y'）$，$ y（t_0）= y_0 $，$ y'（$ y'（t_0）= y'__0 $ $ y'__0 $。这类新方法可以被视为一系列经典的显式伪两步runge-kutta-nyström方法的广义版。 ％新方法将通过GEPTRKN方法表示。我们证明了$ s $ stage geptrkn方法具有准确度的步骤顺序$ p = s $和准确的阶段准确顺序$ r = s $，用于任何一组不同的置列参数$（c_i）_ {i = 1}^s $。如果搭配参数$（c_i）_ {i = 1}^s $满足某些正交性条件，则可以获得这些方法准确性的超级连接。我们证明了$ s $ stage geptrkn方法可以达到准确性顺序$ p = s+2 $。数值实验表明，即使在顺序计算环境中，新方法也比解决非Stiff问题的经典方法更好。通过它们的结构，在并行计算机上实现新方法将更加有效。
A class of explicit pseudo two-step Runge-Kutta-Nyström (GEPTRKN) methods for solving second-order initial value problems $y'' = f(t,y,y')$, $y(t_0) = y_0$, $y'(t_0)=y'_0$ has been studied. This new class of methods can be considered a generalized version of the class of classical explicit pseudo two-step Runge-Kutta-Nyström methods. %The new methods will be denoted by GEPTRKN methods. We proved that an $s$-stage GEPTRKN method has step order of accuracy $p=s$ and stage order of accuracy $r=s$ for any set of distinct collocation parameters $(c_i)_{i=1}^s$. Super-convergence for order of accuracy of these methods can be obtained if the collocation parameters $(c_i)_{i=1}^s$ satisfy some orthogonality conditions. We proved that an $s$-stage GEPTRKN method can attain order of accuracy $p=s+2$. Numerical experiments have shown that the new methods work better than classical methods for solving non-stiff problems even on sequential computing environments. By their structures, the new methods will be much more efficient when implemented on parallel computers.
