Gauss numerical inversion for use in computing the radiation field from a cylindrically symmetric radiation source

Abel inversion of a cylindrically symmetric radiation source involves the s olution of the generalized Abel equations. In this paper, by using the Gaus s numerical integral (GNI), the Abel equation can be separated into a syste m of linear algebraic equations, whose coefficient matrix is an upper trian gle matrix and can be easily solved explicitly. Its numerical solution can achieve second-order accuracy. Three examples are evaluated using the prese nt GNI. It is shown that the high accuracy is achieved and the computed val ues converge to the exact solutions with an increase in the number of nodes . This method is simple and requires less computer time, thus the experimen ters can apply this method easily. (C) 2001 Elsevier Science Ltd. All right s reserved.