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.
Shivanian, E. & Abbasbandy, S. (2018). Multiple solutions of a nonlinear reactive transport model using least square pseudo-spectral collocation method. International Journal of Nonlinear Analysis and Applications, 9(2), 47–57. https://doi.org/10.22075/ijnaa.2017.1538.1402
MLA
Shivanian, E., & Abbasbandy, S. "Multiple solutions of a nonlinear reactive transport model using least square pseudo-spectral collocation method", International Journal of Nonlinear Analysis and Applications, 9, 2, 2018, 47–57. doi: 10.22075/ijnaa.2017.1538.1402
HARVARD
Shivanian, E., & Abbasbandy, S. (2018). 'Multiple solutions of a nonlinear reactive transport model using least square pseudo-spectral collocation method', International Journal of Nonlinear Analysis and Applications, 9(2), pp. 47–57. doi: 10.22075/ijnaa.2017.1538.1402
CHICAGO
Shivanian, E. & Abbasbandy, S., "Multiple solutions of a nonlinear reactive transport model using least square pseudo-spectral collocation method." International Journal of Nonlinear Analysis and Applications, 9 2 (2018): 47–57, doi: 10.22075/ijnaa.2017.1538.1402
VANCOUVER
Shivanian E., Abbasbandy S. Multiple solutions of a nonlinear reactive transport model using least square pseudo-spectral collocation method. IJNAA. 2018;9(2):47–57. doi: 10.22075/ijnaa.2017.1538.1402
International Journal of Nonlinear Analysis and Applications