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Summary.We shall consider an application of simple exponential splines to the numerical solution of singular perturbation problem. The computational effort involved in our collocation method is less than that required for the other methods of exponential type.

Abstract.In this paper it is proved that the two-point boundary value problem, namely (d(4)/dx4 + f)y = g, y(0) -Ax = y(l) -A2 = y"(0) -Bx = y "(I) -B2 = 0, has a unique solution provided infxf(x) = --n > -it4. The given boundary value problem is discretized by a finite difference scheme. This numerical approximation is proved to be a second order convergent process by establishing an error bound using the L2-norm of a vector.