A NUMERICAL-METHOD FOR SINGULAR PERTURBATION PROBLEMS ARISING IN CHEMICAL REACTOR THEORY

A class of singularly perturbed two point boundary value problems for second order ordinary differential equations with mixed boundary conditions, arising in chemical reactor theory is considered. In order to solve them, a numerical method is suggested, in which an exponentially fitted difference scheme is combined with classical numerical methods. The proposed method is distinguished by the following facts: first, we divide the given-interval (the domain of definition of the differential equation) into two subintervals called outer and inner regions. Then, we solve the differential equation over both the regions as two point boundary value problems. The terminal boundary condition of the inner region is obtained using the zero order asymptotic expansion of the solution. Some numerical examples are given to illustrate the method.