波动方程柯西反问题化成线性积分方程的求解方法

A Linearization Approach for the Inverse Problem of the Cauchy Wave Differential Equations

波动方程柯西反问题一般都是化成非线性第二类Fredholm 积分方程求解,由于方程的非线性性质给数值求解带来困难。本文提出一种新方法,即从求基本解入手,将其化成线性积分方程来求解,从而简化了问题.

Generally,the solution of the inverse problem of the Cauchy wave differentialequations is obstained by translating it into nonlinear Fredholem integral equationof the 2nd kind.The nonlinearity of the equation makes numerical calculation diffi-cult.In this paper,a new method is put forward.We begin with solving basic solu-tion and solve this problem by translating it into linear integral equation.So theproblem is simplified.