Technical note Spectral Green's function method for neutron transport: isotropic, forward, and backward scattering in 1-D slab geometry Fikret Anli K.S.U Fen- Ed. Fak. Fizik Bo Èl. 46100, K. Maras Ë, Turkey Received 1 July 2000; accepted 30 August 2000 Abstract Numerical solutions of one-group and one-dimensional neutron transport problems are reportedforisotropic,forward,andbackwardscattering.Numericalsolutioniscarriedoutby using two dierent methods, the SGF `` spectral Green's function '' method and the DD `` diamond-dierence'' scheme, to test the accuracy of the results. Results of cell-edge scalar ¯uxesobtainedforbothmethodsarepresentedinthetables. # 2001ElsevierScienceLtd.All rights reserved. 1. Introduction In recent years, several powerful numerical techniques have been developed to solve the neutron transport equation for which one-dimensional problems are extensive in the literature. Most of the numerical techniques contain spatial dis- cretizations which are based on Taylor series expansion. Therefore, such numerical techniques suer from spatial truncation errors, Lewis and Miller (1984). This meansthat;asthewidthofthespatialcellbecomeslarge,negative¯uxmaybeoccur in the solution. De Barros and Larsen (1990) developed a new numerical method for the one-dimensional neutron transport problem. In this method, the familiar neutron balance equation together with a non-standard auxiliary equation which contains spectral Green's function (SGF) is solved in terms of cell-edge angular ¯uxes. The results are shown to be more accurate than the results obtained from the diamond-dierence (DD) scheme for both homogeneous and heterogeneous problems. Also all calculations are shown to be free from all spatial truncation errors. Annals of Nuclear Energy 28 (2001) 1033±1042 www.elsevier.com/locate/anucene 0306-4549/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved. PII: S0306-4549(00)00105-5