微分方程解的先验估计

Priori Estimates for Solution of Differential Equations

对于给定的二阶线性微分方程的两点边值问题,在工程上利用计算机进行此类微分方程的数值解时,必须考虑数值解是否稳定,算法能否得以实现.为此必须考虑其解的存在性,即讨论它的解是否具有稳定性.针对两点边值问题的二阶线性微分方程的解的估计,运用能量分析法对微分方程的解进行先验估计,并在不同的范数条件下,给出了具体的表达式.

The study of differential equations is one part of mathematics for the second-order linear differential equations with boundary value problem. Its numerical solution of numerical computation in the computer is connected with its theoretical solution. Therefore, we need the steady state solution in the computation. A class of priori estimate is derived by the energy method of analysis for the second-order differential equations with boundary value problem. It is shown that the priori estimate is better than the others in various norms.