Solving differential equations using Sinc-collocation methods with derivative interpolations

Abstract

This paper presents the application of Sinc-collocation method to solve linear second order boundary value problems based on derivative interpolation. Even in the presence of singularities, the Sinc-collocation method is known to exhibit exponential convergence, resulting in highly accurate solutions. However, the customary approaches which involve interpolating the solution variable with the Sinc bases require first and higher order differentiations which induces high sensitivity to numerical errors. In contrast, in this paper, we use first derivative interpolation whose integration is much less sensitive to numerical errors. Moreover, nonhomogeneous derivative based conditions at boundaries are treated with appropriate transformations in order to prevent numerical overflows near boundaries. Unlike previous approaches, the current approach preserves the exponential convergence associated with the Sinc-collocation method.