Sensitivity analysis of boundary value problems: application to nonlinear reaction-diffusion systems

A direct and very efficient approach for obtaining sensitivities of two-point boundary value problems solved by Newton's method is studied. The link between the solution method and the sensitivity equations is investigated together with matters of numerical accuracy and efficiency. This approach is employed in the analysis of a model three species, unimolecular, steady-state, premixed laminar flame. The numerical accuracy of the sensitivities is verified and their values are utilized for interpretation of the model results. It is found that parameters associated directly with the temperature play a dominant role. The system's Green's functions relating dependent variables are also controlled strongly by the temperature. In addition, flame speed sensitivities are calculated and shown to be a special class of derived sensitivity coefficients. Finally, some suggestions for the physical interpretation of sensitivities in model analysis are given.