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

近年来，采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断层扫描等都已广为人知。这些问题所涉及的数学方面称为逆问题。这个问题的特点是一个不适定的问题，其中可能没有明确的解决方案和解决方案，即使它存在，是强烈的影响，只有很小的误差测量。在本研究中，我们提出了一种计算机方法，给出了准确和稳定的答案的反问题。

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.