Year 2021,
, 1527 - 1534, 31.12.2021
Mahmut Modanlı
,
Hüseyin Eş
References
- [1] Pinar, Z., Kocak, H. 2018. Exact solutions for the third-order dispersive-Fisher equations. Nonlinear Dynamics, 91(1), 421-426.
- [2] Ding, L., Ma, W. X., Chen, Q., Huang, Y. 2021. Lump solutions of a nonlinear PDE containing a third-order derivative of time. Applied Mathematics Letters, 112, 106809.
- [3] Rui, W., He, B., Long, Y., Chen, C. 2008. The integral bifurcation method and its application for solving a family of third-order dispersive PDEs. Nonlinear Analysis: Theory, Methods & Applications, 69(4), 1256-1267.
- [4] Manafian, J., Mohammed, SA, Alizadeh, AA, Baskonus, HM ve Gao, W. 2020. Sığ su üzerinde uzun dalgaların yayılmasından kaynaklanan üçüncü dereceden evrim denklemi için yumru ve etkileşiminin araştırılması. European Journal of Mechanics-B/Fluids , 84 , 289-301.
- [5] González-Pinto, S., Hernández-Abreu, D., Pérez-Rodríguez, S., Weiner, R. 2016. A family of three-stage third order AMF-W-methods for the time integration of advection diffusion reaction PDEs. Applied Mathematics and Computation, 274, 565-584.
[6] Zhou, Q., Liu, L., Liu, Y., Yu, H., Yao, P., Wei, C., Zhang, H. 2015. Exact optical solitons in metamaterials with cubic–quintic nonlinearity and third-order dispersion. Nonlinear Dynamics, 80(3), 1365-1371.
- [7] Mary, D. S.1985. Analysis of an implicit finite-difference scheme for a third-order partial differential equation in three dimensions. Computers & Mathematics with Applications, 11(7-8), 873-885.
- [8] Loghmani, G. B., Ahmadinia, M. 2006. Numerical solution of third-order boundary value problems.
- [9] Gordon, R. K., Hutchcraft, W. E. 2001. Higher order wavelet-like basis functions in the numerical solution of partial differential equations using the finite element method. In Proceedings of the 33rd Southeastern Symposium on System Theory (Cat. No. 01EX460) (pp. 391-394). IEEE.
- [10] Chavan, S. S., Panchal, M. M. 2014. Solution of third order Korteweg-De Vries equation by homotopy perturbation method using Elzaki transform. Int J Res Appl Sci Eng Technol, 2, 366-9.
[11] Koksal, M., Koksal, M. E. 2015. Commutativity of cascade connected discrete-time linear time-varying systems. Transactions of the Institute of Measurement and Control, 37(5), 615-622.
- [12] He, J.H. 1999. Homotopy perturbation technique, Comput. Methods Appl. Mech. Engrg. 178, 257.
- [13] He,J.H. 2000. A coupling method of a homotopy technique and a perturbation technique for non-linear problems, Int. J. Non-linear Mech. 35 (1).
Üçüncü Mertebeden Kısmi Diferansiyel Denklemin Homotopy Pertürbasyon Metodu ile Çözümü
Year 2021,
, 1527 - 1534, 31.12.2021
Mahmut Modanlı
,
Hüseyin Eş
Abstract
Bu çalışmada, üçüncü mertebeden kısmi diferansiyel denklemin çözümü homotopy pertürbasyon metodu ile elde edildi. Bu denklemin çözümü için homotopy pertürbasyon metodu oluşturuldu. Bu metot kullanılarak bir örnek problem üzerinde denklemin çözümü bulundu. Elde edilen çözümün tam çözüme denk olduğu görüldü. Matlab programı kullanılarak çözüm için grafikler verildi
References
- [1] Pinar, Z., Kocak, H. 2018. Exact solutions for the third-order dispersive-Fisher equations. Nonlinear Dynamics, 91(1), 421-426.
- [2] Ding, L., Ma, W. X., Chen, Q., Huang, Y. 2021. Lump solutions of a nonlinear PDE containing a third-order derivative of time. Applied Mathematics Letters, 112, 106809.
- [3] Rui, W., He, B., Long, Y., Chen, C. 2008. The integral bifurcation method and its application for solving a family of third-order dispersive PDEs. Nonlinear Analysis: Theory, Methods & Applications, 69(4), 1256-1267.
- [4] Manafian, J., Mohammed, SA, Alizadeh, AA, Baskonus, HM ve Gao, W. 2020. Sığ su üzerinde uzun dalgaların yayılmasından kaynaklanan üçüncü dereceden evrim denklemi için yumru ve etkileşiminin araştırılması. European Journal of Mechanics-B/Fluids , 84 , 289-301.
- [5] González-Pinto, S., Hernández-Abreu, D., Pérez-Rodríguez, S., Weiner, R. 2016. A family of three-stage third order AMF-W-methods for the time integration of advection diffusion reaction PDEs. Applied Mathematics and Computation, 274, 565-584.
[6] Zhou, Q., Liu, L., Liu, Y., Yu, H., Yao, P., Wei, C., Zhang, H. 2015. Exact optical solitons in metamaterials with cubic–quintic nonlinearity and third-order dispersion. Nonlinear Dynamics, 80(3), 1365-1371.
- [7] Mary, D. S.1985. Analysis of an implicit finite-difference scheme for a third-order partial differential equation in three dimensions. Computers & Mathematics with Applications, 11(7-8), 873-885.
- [8] Loghmani, G. B., Ahmadinia, M. 2006. Numerical solution of third-order boundary value problems.
- [9] Gordon, R. K., Hutchcraft, W. E. 2001. Higher order wavelet-like basis functions in the numerical solution of partial differential equations using the finite element method. In Proceedings of the 33rd Southeastern Symposium on System Theory (Cat. No. 01EX460) (pp. 391-394). IEEE.
- [10] Chavan, S. S., Panchal, M. M. 2014. Solution of third order Korteweg-De Vries equation by homotopy perturbation method using Elzaki transform. Int J Res Appl Sci Eng Technol, 2, 366-9.
[11] Koksal, M., Koksal, M. E. 2015. Commutativity of cascade connected discrete-time linear time-varying systems. Transactions of the Institute of Measurement and Control, 37(5), 615-622.
- [12] He, J.H. 1999. Homotopy perturbation technique, Comput. Methods Appl. Mech. Engrg. 178, 257.
- [13] He,J.H. 2000. A coupling method of a homotopy technique and a perturbation technique for non-linear problems, Int. J. Non-linear Mech. 35 (1).