离散正则方法在一维热传导方程寻源反问题中的应用

热传导方程寻源反问题具有不适定性.应用离散正则化方法即用一族与原问题相邻近的适定问题的解去逼近原问题的解,来克服这种不适定性.以一维热传导方程为例,对离散正则化方法进行了阐述,并进行了数值模拟.结果表明离散正则化方法的数值模拟结果与真实结果之间的误差较小,并且随着离散密度的增加,误差越来越小.这种方法避免引入泛函,使用起来较方便,可作为解决热传导方程寻源反问题的有效方法.

Application of discrete regularization method in inverse problem of determining unknown source term in one-dimensional heat conduction equation

In order to solve the ill-posed of heat conduction equation, discrete regularization method is used. It is to use a wellposed question to approach the original question. Take one-dimensional heat conduction equation as the example, discrete regularization method has been elaborated. Value simulation is carried on in this paper. The result indicates that the error between the result of value simulation and the real result is smaller, And along with the increase of separated density, the error is smaller and smaller. This method avoids introducing functional. It is easy to use which will be an effective method to determine the unknown source term in heat conduction equation.