A matrix formulation to the wave equation with non-local boundary condition

Abstract

Recently, various sequential numerical schemes have been proposed for the solution of non-classical hyperbolic initial value problems which involve non-local integral terms over the spatial domain. In this paper, we focus on the wave equation with the non-local boundary condition. Two matrix formulation techniques based on the shifted standard and shifted Chebyshev bases are proposed for the numerical solution. Several numerical examples and also some comparisons with another methods will be investigated to confirm the efficiency of this procedure.

Keywords:

• wave equation
• non-local boundary condition
• matrix formulation
• shifted Chebyshev bases
• shifted standard bases

2000 AMS Subject Classifications :

• 35L05
• 47B40
• 41A30

Acknowledgements

The authors are very grateful to the reviewers for carefully reading the paper and for their constructive comments and suggestions that have improved the paper.

Additional information

Notes on contributors

Babak Soltanalizadeh

Present address:Young Researchers Club, Islamic Azad University, Sarab Branch, Sarab, Iran