‘Shooting method' for singular perturbation problems arising in chemical reactor theory

Abstract

A class of singularly perturbed two-point boundary-value problems for second-order ordinary differential equations arising in chemical reactor theory is considered. In order to solve them numerically, a method is suggested in which the given interval (the domain of the definition of the differential equation) is divided into two subintervals called inner and outer regions. In the inner region an initial-value problem for system of two first-order differential equations is solved based on the uniformly valid exponentially fitted different schemes. The boundary-value problem in the outer region is solved by classical finite difference schemes. A combination of the solution so obtained yields a numerical solution of the boundary-value problem on the whole interval. Error estimates are derived. Numerical examples are presented to illustrate the method. The implementation of the method on parallel architectures is discussed.

Keywords:

• Singular perturbation
• small parameter
• asymptotic expansion
• boundary layer
• exponentially fitted difference scheme
• parallel computation

AMS Subject Classification::

• 65L10

C.R. Categories::

• G1.7