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Fourth order finite-difference algorithms for a semilinear singularly perturbed reaction–diffusion problem are discussed and compared both theoretically and numerically. One of them is the method of Sun and Stynes (1995) which uses a piecewise equidistant discretization mesh of Shishkin type. Another one is a simplified version of Vulanović’s method (1993), based on a discretization mesh of Bakhvalov type. It is shown that the Bakhvalov mesh produces much better numerical results.