Numerical Solution of two-point boundary value problems using Sinc interpolation

摘要

This paper presents the application of Sine method to solve second order two-point boundary value problems based on derivative interpolation. Even in the presence of singularities, the Sine numerical method is known to exhibit exponential convergence, resulting in highly accurate solutions. However, the customary approach of interpolating the solution variable with the Sine bases requires first and higher order differentiations which induce 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, derivative 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 Sine numerical methods.