fitted numerical method for singularly perturbed semilinear three-point boundary value problem

we consider a class of singularly perturbed semilinear threepoint boundary value problems. an accelerated uniformly convergent numerical method is constructed via the exponential fitted operator method using richardson extrapolation techniques to solve the problem. to treat the semilinear term, we use quasilinearization techniques. the numerical results are tabulated in terms of maximum absolute errors and rate of convergence, and it is observed that the present method is more accurate and εuniformly convergent for h ≥ ε, where the classical numerical methods fail to give a good result. it also improves the results of the methods existing in the literature. the method is shown to be secondorder convergent independent of perturbation parameter ε.