Application of Double Aboodh-Shehu Decomposition Method to Solve Linear and Nonlinear System of Partial Differential Equations

Abstract

In this work, we develop a new method to obtain approximate solutions of linear and nonlinear coupled partial differential equations with the help of Double Aboodh-Shehu decomposition method (DASDM). The nonlinear term can easily be handled with the help of Adomian polynomials. The results of the present technique have closed agreement with approximate solutions obtained with the help of Adomian decomposition method (ADM).

Keywords

• Double Aboodh-Shehu decomposition method
• Adomian decomposition method
• linear and nonlinear partial differential equations.

References

1. Aboodh, K.S., Fara, R.A., Almardy, I.A., Almostafa, F.A., Solution of Partial ˙Integro-Differential Equations by using Aboodh and Double Aboodh Transform Methods, Global Journal of Pure and Applied Mathematics, 13(2017), 4347–4360.
2. Aboodh, K.S., The New ˙Integral Transform ”Aboodh Transform”, Global Journal of Pure and Applied Mathematics, 9(2013), 35–43.
3. Albukhuttar, A., Jubear, B., Neamah, M., Solve the Laplace, Poisson and Telegraph equations using the Shehu transform, Turkish Journal of Computer and Mathematics Education, 12(10)(2021), 1759–1768.
4. Alfaqeih, S., Misirli, E., On double Shehu transform and its properties with applications, International Journal of Analysis and Applications, 3(2020), 381–395.
5. Alfaqeih, S., Özis, T., First Aboodh transform of fractional order and its properties, International Journal of Progressive Sciences and Technologies (IJPSAT), 13(2019), 252–256.
6. Eltayeb, H., Kilicman, A., Application of Sumudu decomposition method to solve nonlinear system of partial differential equations, Abstr. Appl. Anal., (2012).
7. Jafari, H., Gejji, V.D., Revised Adomian decomposition method for solving a system of nonlinear equations, Appl. Math. Comput., 174(2006), 1–7.
8. Khalaf, R.F., Belgacem, F.B.M., Extraction of the Laplace, Fourier and Mellin Transforms from the Sumudu Transform, AIP Proceedings, 1637, 1426(2014).

9. Khan, M., Hussain, M., Jafari, H., Khan, Y., Application of Laplace decomposition method to solve nonlinear coupled partial differential equations World Applied Sciences Journal, (2010), 13–19.
10. Maitama, S., Zhao, W., New integral transfrom: Shehu transform ageneralizattion of Sumudu and Laplace transfrom for solving differential equation, International Journal of Analysis and Applications, 174(2019), 167–190.
11. Ouideen, Y., Al-Aati, A., On double Aboodh-Shehu transform and their properties with applications, Journal of Albaydha University, 4(2022), 241–251.
12. Ridha, Z., ALbukhuttar, A., Kadhim, H., Differentiation and integration of Shehu transform, Applied Mathematics, 144(2020), 54553–54560.
13. Sedeeg, A., Mahgoub, M., Comparison of new integral transform Aboodh transform and Adomian decomposition method, Int. J. Math. And App., (4)(2-B)(2016), 127–135.
14. Wazwaz, A.M., Partial Differential Equations and Solitary Waves Theory (1sted.), New York, Springer, 2009.
15. Wazwaz, A.M., A new technique for calculating Adomian polynomials for nonlinear polynomials, Appl. Math. Comput., 111(2002), 33–51.
16. Wazwaz, A.M., Partial Differential Equations Methods and Applications, Netherland Balkema Publisher, 2002.