θ-单支方法的非线性数值稳定性

Nonlinear Numerical Stability of θ-One-Leg Methods

利用一般线性方法的代数稳定性和(k,p,q)-代数稳定性的概念,得到了θ-单支方法数值稳定的代数条件,即当θ≥12时,θ-单支方法是代数稳定和对角稳定的,任给的ε≥0,则θ-单支方法是(1,0,2θ-1-ε)-代数稳定的.

According to algebraic stability and (k,p,q)-algebraic stability of general linear methods, the algebraic conditions of mumerical stability of θ-one-leg methods are obtained,i.e.,θ-one-leg methods is algebraically stable and diagonally stable under the constraint θ≥12,and θ-one-leg methods is (1,0,2θ -1-ε)-algebraically stable for any constant ε ≥ 0.