- - - Department of Applied Mathematics, Faculty of Basic Science, Imam Khomeini International University, Qazvin ۳۴۱۴۹-۱۶۸۱۸, Iran
- - - Department of Applied Mathematics, Faculty of Basic Science, Imam Khomeini International University, Qazvin ۳۴۱۴۹-۱۶۸۱۸, Iran

The recognition and the calculation of all branches of solutions of the nonlinear boundary value problems is difficult obviously. The complexity of this issue goes back to the being nonlinearity of the problem. Regarding this matter, this paper considers steady state reactive transport model which does not have exact closed-form solution and discovers existence of dual or triple solutions in some cases using a new hybrid method based on pseudo-spectral collocation in the sense of least square method. Furthermore, the method usages Picard iteration and Newton method to treat nonlinear term in order to obtain unique and multiple solutions of the problem, respectively.

Pseudo-spectral collocation method, Least square method, Newton iteration method, Picard iteration, Chebyshev-Gauss-Lobatto points