Abstract
The Gardner equation is commonly used to describe wave propagation in weakly nonlinear dispersive medium. The Gardner equation has a higher order nonlinear term, which could make the numerical calculation inaccurate. In this paper, the Gardner equation is solved using two numerical methods, i.e., the method of lines and pseudospectral method. The efficiency and accuracy of both methods were studied. Our results show that both methods are accurate and efficient methods to solve the Gardner equation. By comparing the accuracy of both the methods, the method of lines performs better than pseudospectral method most of the time.
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Acknowledgments
This work was supported by Universiti Malaysia Sarawak through Small Grant Scheme—01(S128)/1022/2013(12) and RAGS R026 Universiti Tun Hussein Onn. The authors would also like to thank Universiti Teknologi Malaysia for providing the resources used in the conduct of this study.
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Tiong, W.K., Tay, K.G., Ong, C.T., Sze, S.N. (2017). Numerical Solution of the Gardner Equation. In: Ahmad, AR., Kor, L., Ahmad, I., Idrus, Z. (eds) Proceedings of the International Conference on Computing, Mathematics and Statistics (iCMS 2015). Springer, Singapore. https://doi.org/10.1007/978-981-10-2772-7_25
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DOI: https://doi.org/10.1007/978-981-10-2772-7_25
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Online ISBN: 978-981-10-2772-7
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