Convergence analysis of compact finite difference method for the solution of anti-periodic boundary value problems

The main objective of this paper is to introduce the fourth and sixth-order compact finite difference methods for solving anti-periodic boundary value problems. Compact finite difference formulas can approximate the derivatives of a function more accurately than the standard finite difference formulas for the same number of grid points. The convergence analysis of the proposed method is also investigated. This analysis shows how the error between the approximate and exact solutions decreases as the grid space is reduced.  To validate the proposed method's accuracy and efficiency, some computational experiments are provided. Moreover, a comparison is performed between the standard and compact finite difference methods.  The experiments indicate that the compact finite difference method is more accurate and efficient than the standard one.