Solving Multi-Point Boundary Value Problems Using Sinc-Derivative Interpolation

Abstract

In this paper, the Sinc-derivative collocation method is used to solve linear and nonlinear multi-point boundary value problems. This is done by interpolating the first derivative of the unknown variable via Sinc numerical methods and obtaining the desired solution through numerical integration of the interpolation and all higher order derivatives through successive differentiation of the interpolation. Non-homogeneous boundary conditions are reduced to homogeneous using suitable transformations. The efficiency and the accuracy of the method are tested using illustrative examples previously considered by other researchers who used different approaches. The results show the excellent performance of the Sinc-derivative collocation method.

Keywords

• multi-point boundary value problems
• sinc-collocation
• sinc-derivative
• numerical methods
• differential equations