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Journal of Applied Mathematics and Computation

ISSN Online: 2576-0653 ISSN Print: 2576-0645 CODEN: JAMCEZ
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ArticleOpen Access http://dx.doi.org/10.26855/jamc.2020.06.004

Application of the Adomian Decomposition Method to the Solution of the Linear Nonhomogeneous One-Dimensional Wave Equation

Christian Kasumo

Department of Science and Mathematics, Mulungushi University, P.O. Box 80415, Kabwe, Zambia.

*Corresponding author: Christian Kasumo

Published: July 07, 2020

Abstract

The Adomian decomposition method is employed in the solution of the linear nonhomogeneous one-dimensional wave equation. This method leads to an analytical solution in the form of an infinite power series. A comparison of the results obtained by the numerical method with the exact solution from d’Alembert’s formula shows the high degree of accuracy of the Adomian decomposition method.

Keyword

Nonhomogeneous wave equation, Adomian decomposition method, D’Alembert’s formula

References

[1] Lamb Jr., G. L. (1995). Introductory Applications of Partial Differential Equations with Emphasis on Wave Propagation and Diffusion. John Wiley and Sons, New York.

[2] Tyn, M. U. (1980). Partial Differential Equations of Mathematical Physics. Cambridge University Press, Cambridge.

[3] Constanda, C. (2002). Solution Techniques for Elementary Partial Differential Equations. CRC Press, New York.

[4] Duffy, D. G. (2004). Transform Methods for Solving Partial Differential Equations. CRC Press, New York.

[5] Hu, W. (2017). A New Method to Solve Non-homogeneous Wave Equations of Electromagnetic Fields by Fourier’s Triple Integral Transform. Proceedings of 2nd International Conference on Materials Science, Energy Technology and Environmental Engineering, 81, 28-30.

[6] Kiliçman, A. and Eltayeb, H. (2007). A Note on the Non-constant Coefficient Linear Second Order Partial Differential Equation. Proceedings of the Fourth International Conference of Applied Mathematics and Computing, Plovdiv, Bulgaria, 12-18 August, 2007.

[7] Babakhani, A. and Dahiya, R. S. (2001). Systems of Multi-dimensional Laplace Transform and Heat Equation. In: 16th Conference on Applied Mathematics, University of Central Oklahoma, Electronic Journal of Differential Equations Conference, 7, 25-36.

[8] Kasumo, C. (2019). Solving the Linear Homogeneous One-Dimensional Wave Equation Using the Adomian Decomposition Method. Applied Mathematical Sciences, 13(5), 239-252.

[9] Sun, Z. (2001). A High Order Difference Scheme for a Nonlocal Boundary Value Problem for the Heat Equation. Computational Methods in Applied Mathematics, 1, 398-414.

[10] Adomian, G. (1994). Solving Frontier Problems of Physics: The Decomposition Method. Springer, New York.

[11] Adomian, G. and Rach, R. (1992). Noise Terms in Decomposition Solution Series. Comp. Math. Appl., 24(11), 61-64.

[12] Wazwaz, A.-M. (1997). Necessary Conditions for the Appearance of Noise Terms in Decomposition Solution Series. J. Math. Anal. Appl., 5, 265-274.

[13] Kaya, D. and Inc, M. (1999). On the Solution of the Non-linear Wave Equation by the Decomposition Method. Bull. Malaysian Math. Soc. (second series), 22, 151-155.

[14] Almazmumy, M., Hendi, F. A., Bakodah, H. O. and Alzumi, H. (2012). Recent Modifications of Adomian Decomposition Method for Initial Value Problem in Ordinary Differential Equations. American J. Comput. Math., 2, 228-234.

[15] Hopkins, R. (2016). Nonlinear Wave Equations. University of Chicago, 1-14.

[16] Rach, R., Adomian, G. and Meyers, R. E. (1992). A Modified Decomposition. Comput. Math. Appl., 23, 17-23.

[17] Wazwaz, A.-M. (1999). A Reliable Modification of Adomian Decomposition Method. Appl. Math. Comput., 102, 77-86.

[18] Biazar, J. and Hosseini, K. (2016). A modified Adomian Decomposition Method for Singular Initial Value Emden-Fowler Type Equations. Int. J. Appl. Math. Research, 5(1), 69-72.

[19] Alderremy, A. A., Elzaki, T. M. and Chamekh, M. (2019). Modified Adomian Decomposition Method to Solve Generalized Emden-Fowler Systems for Singular IVP. Mathematical Problems in Engineering, 2019, 1-6.

Copyright

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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives (CC BY-NC-ND) license, which permits non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited and is not modified or adapted.
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How to cite this paper

Application of the Adomian Decomposition Method to the Solution of the Linear Nonhomogeneous One-Dimensional Wave Equation

How to cite this paper: Christian Kasumo. (2020) Application of the Adomian Decomposition Method to the Solution of the Linear Nonhomogeneous One-Dimensional Wave Equation. Journal of Applied Mathematics and Computation, 4(2), 34-42.

DOI: http://dx.doi.org/10.26855/jamc.2020.06.004