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A family of tridiagonal formally fourth-order difference schemes is developed for a class of singular perturbation problems. These schemes have no cell Reynolds number limitation and satisfy a discrete maximum principle. Error estimates and numerical results for this family of methods are given, and are compared with those for several other schemes.doi:10.1090/s0025-5718-1980-0572850-8 fatcat:pr35ckcqzrdobezk7x4xyv7yw4