关于“追赶”法的稳定性

序言 用差分方程逼近常微分方程边值问题,或用隐式差分格式逼近演化型偏微分方程初边值问题时,通常需求解差分方程的两点边值问题.常用的方法是“追赶法”.在1—4]中,讨论了各种类型的“追赶”法及其稳定性.在这些文章中,或依据系数矩阵特征值的性质,或依据差分方程两点边值问题在C模意义下的性态,来证明“追赶”法的稳定性.关于差分

ON THE STABILITY OF DOUBLE SWEEP METHODS

In this paper, the stability of double sweep methods is discussed. If the two-pointboundary value problem of system of differenee equations is well conditioned in l~2-norm and the approximate coefficient matrices of double sweep method are uniformlybounded and uniformly nonsingular, then the method is stable. For the mixed initial-boundary-value problems for hyperbolic system of first-orderpartial differential equations, if the implicit difference scheme is stable in l~2-norm,then the double sweep method used for its solution is always stable Under the conditionof the approximate coefficient inatrices mentioned above. And this condition concern-ing the coefficient matrices can always be satisfied by choosing appropriate matrixregulators.