This study introduces a stable central difference method for solving second-order
self-adjoint singularly perturbed boundary value problems. First, the solution
domain is discretized. Then, the derivatives in the given boundary value problem
are replaced by finite difference approximations and the numerical scheme that
provides algebraic systems of equations is developed. The obtained system of
algebraic equations is solved by Thomas algorithm. The consistency and stability
that guarantee the convergence of the scheme are investigated. The established
convergence of the scheme is further accelerated by applying the Richardson
extrapolation which yields sixth order convergent. To validate the applicability of
the method, two model examples are solved for different values of perturbation
parameter ε and different mesh size h. The proposed method approximates the
exact solution very well. Moreover, the present method is convergent and gives
more accurate results than some existing numerical methods reported in the
literature.