A computational method for solving singular perturbation problems using exponentially fitted finite difference schemes

摘要

A computational method is presented for solving linear singularly perturbed two point boundary value problems with a boundary layer on the left end of the interval. The original problem is divided into inner and outer region problems. The zeroth-order asymptotic expansion is used to obtain the terminal boundary condition. Then, a new inner region problem (IRP) is created and solved as a two-point boundary value problem (TPBVP). In turn, the outer region problem (ORP) is also solved as a TPBVP. Both these problems (TPBVPS) are efficiently solved by employing uniform and optimal exponentially fitted finite difference schemes.