Implicit midpoint rule and extrapolation to singularly perturbed boundary value problems

Linear singularly perturbed boundary value problem epsilon y(n) - py =f(x), y(0) = y(l) = 0 is solved numerically by reducing to the first order linear system and applying the implicit midpoint rule on equidistant meshes, Using the asymytotic expansion of the global error, the second order of convergence is improved by Richardson extrapolation when h(2) less than or equal to epsilon. Some numerical examples are given in illustration of this theory.