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

Yıl 2024, , 217 - 228, 30.06.2024
https://doi.org/10.47000/tjmcs.1372574

Öz

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).

Kaynakça

  • 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.
  • Aboodh, K.S., The New ˙Integral Transform ”Aboodh Transform”, Global Journal of Pure and Applied Mathematics, 9(2013), 35–43.
  • 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.
  • Alfaqeih, S., Misirli, E., On double Shehu transform and its properties with applications, International Journal of Analysis and Applications, 3(2020), 381–395.
  • 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.
  • Eltayeb, H., Kilicman, A., Application of Sumudu decomposition method to solve nonlinear system of partial differential equations, Abstr. Appl. Anal., (2012).
  • Jafari, H., Gejji, V.D., Revised Adomian decomposition method for solving a system of nonlinear equations, Appl. Math. Comput., 174(2006), 1–7.
  • Khalaf, R.F., Belgacem, F.B.M., Extraction of the Laplace, Fourier and Mellin Transforms from the Sumudu Transform, AIP Proceedings, 1637, 1426(2014).
  • 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.
  • 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.
  • Ouideen, Y., Al-Aati, A., On double Aboodh-Shehu transform and their properties with applications, Journal of Albaydha University, 4(2022), 241–251.
  • Ridha, Z., ALbukhuttar, A., Kadhim, H., Differentiation and integration of Shehu transform, Applied Mathematics, 144(2020), 54553–54560.
  • 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.
  • Wazwaz, A.M., Partial Differential Equations and Solitary Waves Theory (1sted.), New York, Springer, 2009.
  • Wazwaz, A.M., A new technique for calculating Adomian polynomials for nonlinear polynomials, Appl. Math. Comput., 111(2002), 33–51.
  • Wazwaz, A.M., Partial Differential Equations Methods and Applications, Netherland Balkema Publisher, 2002.
Yıl 2024, , 217 - 228, 30.06.2024
https://doi.org/10.47000/tjmcs.1372574

Öz

Kaynakça

  • 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.
  • Aboodh, K.S., The New ˙Integral Transform ”Aboodh Transform”, Global Journal of Pure and Applied Mathematics, 9(2013), 35–43.
  • 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.
  • Alfaqeih, S., Misirli, E., On double Shehu transform and its properties with applications, International Journal of Analysis and Applications, 3(2020), 381–395.
  • 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.
  • Eltayeb, H., Kilicman, A., Application of Sumudu decomposition method to solve nonlinear system of partial differential equations, Abstr. Appl. Anal., (2012).
  • Jafari, H., Gejji, V.D., Revised Adomian decomposition method for solving a system of nonlinear equations, Appl. Math. Comput., 174(2006), 1–7.
  • Khalaf, R.F., Belgacem, F.B.M., Extraction of the Laplace, Fourier and Mellin Transforms from the Sumudu Transform, AIP Proceedings, 1637, 1426(2014).
  • 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.
  • 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.
  • Ouideen, Y., Al-Aati, A., On double Aboodh-Shehu transform and their properties with applications, Journal of Albaydha University, 4(2022), 241–251.
  • Ridha, Z., ALbukhuttar, A., Kadhim, H., Differentiation and integration of Shehu transform, Applied Mathematics, 144(2020), 54553–54560.
  • 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.
  • Wazwaz, A.M., Partial Differential Equations and Solitary Waves Theory (1sted.), New York, Springer, 2009.
  • Wazwaz, A.M., A new technique for calculating Adomian polynomials for nonlinear polynomials, Appl. Math. Comput., 111(2002), 33–51.
  • Wazwaz, A.M., Partial Differential Equations Methods and Applications, Netherland Balkema Publisher, 2002.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Kısmi Diferansiyel Denklemler
Bölüm Makaleler
Yazarlar

Alı Al-aatı 0000-0001-5835-6286

Wedad Al-sharaı Bu kişi benim 0009-0003-3990-6563

Yayımlanma Tarihi 30 Haziran 2024
Yayımlandığı Sayı Yıl 2024

Kaynak Göster

APA Al-aatı, A., & Al-sharaı, W. (2024). Application of Double Aboodh-Shehu Decomposition Method to Solve Linear and Nonlinear System of Partial Differential Equations. Turkish Journal of Mathematics and Computer Science, 16(1), 217-228. https://doi.org/10.47000/tjmcs.1372574
AMA Al-aatı A, Al-sharaı W. Application of Double Aboodh-Shehu Decomposition Method to Solve Linear and Nonlinear System of Partial Differential Equations. TJMCS. Haziran 2024;16(1):217-228. doi:10.47000/tjmcs.1372574
Chicago Al-aatı, Alı, ve Wedad Al-sharaı. “Application of Double Aboodh-Shehu Decomposition Method to Solve Linear and Nonlinear System of Partial Differential Equations”. Turkish Journal of Mathematics and Computer Science 16, sy. 1 (Haziran 2024): 217-28. https://doi.org/10.47000/tjmcs.1372574.
EndNote Al-aatı A, Al-sharaı W (01 Haziran 2024) Application of Double Aboodh-Shehu Decomposition Method to Solve Linear and Nonlinear System of Partial Differential Equations. Turkish Journal of Mathematics and Computer Science 16 1 217–228.
IEEE A. Al-aatı ve W. Al-sharaı, “Application of Double Aboodh-Shehu Decomposition Method to Solve Linear and Nonlinear System of Partial Differential Equations”, TJMCS, c. 16, sy. 1, ss. 217–228, 2024, doi: 10.47000/tjmcs.1372574.
ISNAD Al-aatı, Alı - Al-sharaı, Wedad. “Application of Double Aboodh-Shehu Decomposition Method to Solve Linear and Nonlinear System of Partial Differential Equations”. Turkish Journal of Mathematics and Computer Science 16/1 (Haziran 2024), 217-228. https://doi.org/10.47000/tjmcs.1372574.
JAMA Al-aatı A, Al-sharaı W. Application of Double Aboodh-Shehu Decomposition Method to Solve Linear and Nonlinear System of Partial Differential Equations. TJMCS. 2024;16:217–228.
MLA Al-aatı, Alı ve Wedad Al-sharaı. “Application of Double Aboodh-Shehu Decomposition Method to Solve Linear and Nonlinear System of Partial Differential Equations”. Turkish Journal of Mathematics and Computer Science, c. 16, sy. 1, 2024, ss. 217-28, doi:10.47000/tjmcs.1372574.
Vancouver Al-aatı A, Al-sharaı W. Application of Double Aboodh-Shehu Decomposition Method to Solve Linear and Nonlinear System of Partial Differential Equations. TJMCS. 2024;16(1):217-28.