Partial Differential Equations of Hyperbolic Type
Partial Differential Equations of Hyperbolic Type
复制标题
双曲型偏微分方程
DOI：
10.1007/978-3-0348-7922-4_6
复制
发表时间：
2004
期刊：
影响因子：
--
通讯作者：
P. Sobolevskiĭ
中科院分区：
文献类型：
--
作者：
A. Ashyralyev;P. Sobolevskiĭ
在这一章中，我们考虑了任意Banach空间中抛物型微分方程v '（t）+ A（t）v（t）= f（t）（0 \leqslant t \leqslant T），v（0）= {{v}_{0}}$$的抽象Cauchy问题的适定性。给出了该问题数值解的精确差分格式和两点Taylor分解的高精度差分格式。研究了这些差分格式在各种Banach空间中的适定性。得到了抛物型方程混合型边值问题高阶差分格式解的稳定性和强制稳定性的保持器模估计.
In the present chapter we consider the well-posedness of an abstract Cauchy problem for differential equations of parabolic type, $$v'(t) + A(t)v(t) = f(t)(0 \leqslant t \leqslant T),v(0) = {{v}_{0}}$$ in an arbitrary Banach space with the linear positive operatorsA(t). The high order of accuracy difference schemes generated by an exact difference scheme or by Taylor’s decomposition on two points for the numerical solutions of this problem are presented. The well-posedness of these difference schemes in various Banach spaces are studied. The stability and coercive stability estimates in Holder norms for the solutions of the high order of accuracy difference schemes of mixed type boundary-value problems for parabolic equations are obtained.