Unfolding algorithms for neutron depth profiling:probability iteration, SVD solving least square, linear regularization(LR) and constrained linear reqularization(CLR) are studied. All algorithms are applied for both under-determined and over-determined equations, and results are compared and discussed. Due to iterative processes, probability iteration and CLR could not work well in the case that sources intensities change sharply. LR is unstable as unfolding range is chosen arbitrarily, which can be constrained by CLR. A practical spectrum of NDP experiment is unfolded by algorithms. LR could not restrain stochastic errors caused by statistical fluctuation, while other algorithms show good unfolding results and agree well with references.

Strategy of detailed history method is summarized, depending on which code ITR(ions transport and reaction) was developed. Both basic method and impulse approximation method to select flight path of ions are complemented respectively. Numerical results agree with CORTEO and TRIM very well. Relation between two methods is discussed. We found reason of CORTEO results differ from TRIM's by limiting maximum of flight length derived by impluse approximation method. ITR has advantages of TRIM and CORTEO. Impluse approximation method reduces nuclear collisions simulated. Index technique is used to calculate scattering angle, which significantly improves efficiency of ITR.

Principles of ion interaction with target atoms including nucleus and electrons are introduced. We study "detail history" Monte Carlo method. An ion Monte Carlo simulation code ITR (ions transport and reaction) was developed. It shows that our code perform good results compared with TRIM and Corteo. It is faster than TRIM.

For NDP,we produce an iteration method derived from probability iteration.It is compared with linear regularization(LR) method for unfolding of NDP.Both produce good results without counts random errors.Iteration method's result is none-negative.LR method is better at the position where source distributions change steeply.Iteration method produce better results as we consider count random errors.It shows that amplifying matrix elements exponentially brings acceleration.