Sinc–Galerkin method based on the DE transformation for the boundary value problem of fourth-order ODE

In this paper a Sinc–Galerkin method incorporated with the double exponential transformation (abbreviated as the DE transformation) for the two-point boundary value problem of fourth-order ordinary differential equation is considered. In this method the error bound O ( exp ( - c ′ N / log N ) ) ( c ′ > 0 ) is attained as in the Sinc-collocation method based on the DE transformation where N is a parameter representing the number of terms in the Sinc approximation. High efficiency of the Sinc–Galerkin method with the DE transformation is confirmed by some numerical examples and the numerical results were compared with ones obtained by Sinc-collocation method based on the DE transformation.