ANALYTICAL APPROXIMATE SOLUTIONS OF CERTAIN NONLINEAR EQUATIONS OF REACTION-DIFFUSION KIND

Monotone iterative procedures are used to obtain analytical approximate solutions of a certain family of nonlinear heterogeneous reaction-diffusion problems. Upper and lower bounds are also obtained and used to test the accuracy of the method. Approximate solutions and bounds are obtained solving a sequence of linear PDE systems which are constructed replacing the nonlinear functions present in the original problem by adequate approximating expressions in terms of the independent variables. For the choice of approximating functions made in this paper, the method proves to be useful for engineering applications in the range of parameters where asymptotic solutions are not accurate.