The Correct Formulation of Intermediate Boundary Conditions for Runge-Kutta Time Integration of Initial Boundary Value Problems
The Correct Formulation of Intermediate Boundary Conditions for Runge-Kutta Time Integration of Initial Boundary Value Problems
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DOI：
10.1137/s1064827594273948
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发表时间：
1997-09
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影响因子：
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通讯作者：
D. Pathria
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文献类型：
--
作者：
D. Pathria
将显式高阶Runge—Kutta （RK）时间积分器应用于由直线法求解的初始边值问题时，一个令人不安的特点是由于中间阶段边界条件的错误规范而导致精度损失。这里提出的解决方案是解析地规定在边界处应用RK求解器所产生的值，从而在不减少步长限制的情况下保持RK方法的阶数。对非线性双曲方程进行了详细的描述，并给出了标量和矢量的例子。
A disturbing feature of applying explicit high-order Runge--Kutta (RK) time integrators to initial boundary value problems solved by the method of lines is the loss of accuracy that results from wrong specifications of intermediate-stage boundary conditions. The solution proposed here is to prescribe analytically those values that would result from applying the RK solver at the boundaries, and hence maintain the order of the RK method without a reduction in the step size limit. The procedure is described in detail for nonlinear hyperbolic equations, and both scalar and vector examples are presented.