Keywords

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.