Double exponential transformation in the Sinc-collocation method for a boundary value problem with fourth-order ordinary differential equation

In this paper we consider a Sinc-collocation method for the two-point boundary value problem of fourth-order ordinary differential equation incorporated with the double exponential transformation (abbreviated as the DE transformation). By this method a convergence rate O(exp(-cN/logN)) where N is a parameter representing the number of terms in the Sinc approximation is attained. We compared the result with ones based on the single exponential transformation which made us confirm the high efficiency of the present method.