Development of highly accurate numerical method based on finite differences and its application to ill-posed problems of partial differential equations.

近年来，矿业中的自然资源探测、工程中的无损检测、医学诊断中的计算机层析成像等已广为人知。这些问题所涉及的数学方面称为反问题。这个问题的特点是不适定的问题，在这个问题中可能没有确定的解，即使有解，也只受测量中的小误差的强烈影响。在目前的研究中，我们提出了一种计算机方法，给出了反问题的准确和稳定的答案。

Recently natural resource probe in the mining industry, nondestructive testing in engineering, computer tomography in medical diagnosis, and so on are widely known. The mathematical aspect involved in these issues are called inverse problem. The problem is featured by an ill-posed problem in which there may be no definite solution and the solution, even if it exists, is strongly influenced by only small errors in the measurement. In the present research we proposed a computer method that gives accurate and stable answers to the inverse problem.