浅谈解的存在唯一性定理在《偏微分方程数值解》中的应用

Application of the Numerical Methods for Partial Differential Equations of Solution's Existence and Uniqueness Theorem

从一个新的角度讨论常微分方程中解的存在唯一性定理在偏微分方程数值解法中的重要应用。给出一类伪双曲型偏微分方程的新的分裂混合有限元数值格式,将该格式转化成常微分方程系统,利用解的存在唯一性定理证明该系统是存在唯一解的。通过简短的讨论、概述明确解的存在唯一定理在偏微分方程数值解中的应用方法,并希望能够在教学科研未来的发展中有新的观念。

Discusses an important application in the numerical methods for partial differential equations of the solution＇s existence and uniqueness theorem of ordinary differential equations by a new perspective. Gives a new splitting mixed element scheme for a class of pseudo-hyper- bolic partial differential equations, formulate the system of ordinary differential equations, proves the solution＇s existence and uniqueness of system by the solution＇s existence and uniqueness theorem. By the brief discussion and outlining, clarifies the application method in the numerical methods for partial differential equations of the solution＇s existence and uniqueness theorem and hopes to have some new ideas in the future development of teaching and research.