- - - Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City (۱۱۸۸۴), Cairo, Egypt
- - - Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City (۱۱۸۸۴), Cairo, Egypt
- - - Mathematics Department, Faculty of Science, Menoufia University, Shebein El-Koom, Egypt.

The non-local hyperbolic partial differential equations have many applications in sciences and engineering. A collocation finite element approach based on exponential cubic B-spline and quintic B-spline are presented for the numerical solution of the wave equation subject to nonlocal boundary condition. Von Neumann stability analysis is used to analyze the proposed methods. The efficiency, accuracy and stability of the methods are assessed by applying it to the test problem. The results are found to be in good agreement with known solutions and with existing collocation schemes in literature.

Collocation methods, Exponential cubic B-spline, Quintic B-spline, Finite difference, Wave equation