Parametric differentiation technique applied to a combustion problem

The parametric differentiation technique - requiring one known (exact/true) solution for a specified set of parameters, and usually with the solution obtained for extreme or limiting values of the parameters - is applied to a class of combustion problems. The problem considered presents a range of integration from minus infinity to plus infinity, with gradients zero at both ends of the boundary, so that linearized equations are difficult to solve. The noniterative parametric differentiation is combined with integration from zero on both sides to (minus/plus) infinity.