An efficient Sinc-collocation method via the DE transformation for eighth-order boundary value problems

This paper shows the exponential convergence of the Sinc-collocation method based on the double exponential (DE) transformation applied to eighth-order boundary value problems (BVPs). Then using Kantorovich's theorem, we obtain the exponential convergence of the non-linear eighth-order ordinary differential equation (ODE). Furthermore, we extend the analytical results to the arbitrary even-order case. In the numerical experiment, several linear and nonlinear examples are provided to verify our theoretical analysis. Meanwhile, the solution yielded via DE transformation is compared with those obtained by single exponential (SE) transformation and existing method to demonstrate the high efficiency and accuracy of our method. (c) 2022 Elsevier B.V. All rights reserved.