线性初边值问题差分格式的稳定性和收敛性(英文)

本文讨论一般的方程系数满足Lipschitz条件的变系数线性双曲型初边值问题差分格式的稳定性,并在很弱的条件下证明了几类差分格式是稳定的,本文还证明了:如果格式稳定,则在解和方程的系数足够光滑时,差分解将收敛于微分方程的解,并且g阶格式在l_2空间有g阶收敛速度。

STABILITY AND CONVERGENCE OF DIFFERENCE SCHEMES FOR LINEAR INITIAL-BOUNDARY-VALUE PROBLEMS

In this paper, we deal with stability of difference schemes for initial-boundary-valueproblems of general linear hyperbolic systems with variable coefficients satisfying the Lipschitzcondition, and prove under very weak conditions that several classes of difference schemes arestable. We also prove that if a q-th order scheme is stable, the approximate solution obtainedby using the scheme converges to the true solution, and the rate of convergence in L_2 is q-orderwhen the solution and the coefficients of partial differential equations are sufficiently smooth.