Abel变换的数值反演

Numerical Inversion of Abel Transform

考虑Abel变换的数值反演问题,由于新的数值微分方法的引入,以及对反演公式中奇异积分的合理处理,使得反演能够获得稳定的结果.理论及数值结果都显示方法是十分有效的.

This paper discusses a problem of numerical inversion of Abel transform. A new method for numerical differentiation is introduced. A reasonable method to deal with singular integral is given. The theoretical results and numerical examples show that the proposed method is effective.