Fourth Order Compact Finite Difference Method for Solving One Dimensional Wave Equation

Abstract

This paper introduces the fourth order compact finite difference method for solving the numerical solution of one-dimensional wave equations. The convergence of the method for the problem under consideration had been investigated. To validate the applicability of the method on the proposed equation, two model examples have been solved for different values of mesh sizes. The numerical results in terms of point wise absolute errors presented in tables and graphs show that the present method approximates the exact solution very well.

Keywords

• Wave equation,Compact finite difference method,Consistence

References

1. [1] Jain M.K., Iyengar S.R.K, Jain R. K., computational methods for partial differential equations, New age international publishers, 2007.
2. [2] Zafar Z. U., Pervaiz A., Ahmed M.O. and Rafiq M., Finite Element Model for Linear Second Order One Dimensional Inhomogeneous Wave Equation, Pak. J. Engg. & Appl. Sci. Vol. 17, Jul., 2015 (p. 58–63).
3. [3] Rajni Arora, Suruchi Singh, Swarn Singh, Exponential B-Spline Collocation Method For The Numerical Solution Of One-Space Dimensional Nonlinear Wave Equation With Strong Stability Preserving Time Integration, 2nd international conference on recent innovations in science, engineering and management, 22 November 2015, www.conferencewarld.in ISBN: 978-81-931039-9-9.
4. [4] Abbas Saadatmandi, Mehdi Dehghan, Numerical Solution of the One-dimensional Wave Equation with an Integral Condition, Published online 14 July 2006 in Wiley Inter Science (www.interscience.wiley.com). DOI 10.1002/num.20177.
5. [5] Rashidinia J. and Mohsenyzadeha, Numerical Solution of One-Dimensional Heat and Wave Equation by Non-Polynomial Quintic Spline, International Journal of Mathematical Modelling & Computations Vol. 05, No. 04, ( 2015), 291- 305.
6. [6] Won Y. Yang, Wenwu Cao, Tae-Sang Chung, John Morris, Applied Numerical methods using MATLAB, Wiley student Edition, 2013.