Numerical studies of non-local hyperbolic partial differential equations using collocation methods

Document Type : Research Paper

Authors

1 Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt

2 Mathematics Department, Faculty of Science, Menoufia University, Shebein El-Koom, Egypt.

Abstract

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.

Keywords


Volume 6, Issue 3
July 2018
Pages 326-338
  • Receive Date: 09 January 2018
  • Revise Date: 16 April 2018
  • Accept Date: 14 May 2018
  • First Publish Date: 01 July 2018