单支方法的保单调性

Monotonicity-preserving One-leg Methods

保单调的时间离散方法求解具有非连续解的双曲型守恒律是一种常用而且有效的算法,空间离散化双曲型守恒律可得到相应的常微分方程初值问题。研究了单支方法求解上述常微分方程初值问题的非线性稳定性质,分析了单支方法的保单调性。将单支方法写为一般线性方法的形式,在步长满足一定约束条件的情况下,获得了单支方法保单调的充分条件。

Monotonicity preserving time discretizations have popular and effective algorithms for the seminorm of hyperbolic laws with discontinuous solution. Nonlinear stability property of one-leg methods were investigated for initial value problems of ordinary differential equations that arise from the semi-discretization of （hyperbolic） partial differential equations. One-leg method was rewritten as general linear method. A sufficient condition for one-leg methods to be monotonicity preserving was given under certain stepsize restriction.