论文标题
稳定的显式亚当型型方法
Stabilized explicit Adams-type methods
论文作者
论文摘要
在这项工作中，我们提出具有扩展稳定性间隔的明确的ADAMS-TYPE多步法方法，该方法类似于稳定的Chebyshev runge-Kutta方法。事实证明，对于任何$ k \ geq 1 $，都存在明显的$ k $ - 步骤adams-type订单方法，其稳定性间隔为$ 2K $。一阶方法的系数和误差常数具有非常简单的表达式。得出了这些方法的阻尼修改。在通常的情况下，要构建$ k $ step的订单$ p $的方法，必须解决一个约束优化问题，其中目标函数和$ p $约束是$ k $变量中的第二级多项式。我们计算高阶方法，直至六个数值订购，并执行一些数值实验以确认方法的准确性和稳定性。
In this work we present explicit Adams-type multistep methods with extended stability interval, which are analogous to the stabilized Chebyshev Runge--Kutta methods. It is proved that for any $k\geq 1$ there exists an explicit $k$-step Adams-type method of order one with stability interval of length $2k$. The first order methods have remarkably simple expressions for their coefficients and error constant. A damped modification of these methods is derived. In general case to construct a $k$-step method of order $p$ it is necessary to solve a constrained optimization problem in which the objective function and $p$ constraints are second degree polynomials in $k$ variables. We calculate higher-order methods up to order six numerically and perform some numerical experiments to confirm the accuracy and stability of the methods.
