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

近年来，自然资源探测在采矿业中的应用、无损检测在工程中的应用、计算机断层扫描在医学诊断中的应用等都得到了广泛的认识。涉及这些问题的数学方面被称为逆问题。这个问题的特点是不适定问题，其中可能没有确定的解，即使存在解，也只受测量中的小误差的强烈影响。在本研究中，我们提出了一种计算机方法，可以给出精确而稳定的反问题答案。

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.