“Shooting method” for the solution of singularly perturbed two-point boundary-value problems having less severe boundary layer

摘要

Singularly perturbed two-point boundary-value problems (BVPs) having less severe boundary layers are considered. A method is presented in this paper to solve these problems numerically. The domain of definition of the differential equation is divided into two subintervals. In one subinterval (inner region) an initial-value problem (IVP) obtained from the given BVP is solved by an exponentially fitted difference (EFD) scheme, whereas a classical upwind scheme is used to solve the BVP in the other subinterval (outer region). In order to obtain initial and boundary conditions, an asymptotic approximation is used. Error estimates are derived for the numerical solution. The implementation of the method on parallel architectures is discussed. Numerical results are also presented in support of the proposed method.