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Hamzah Mahdi Abedi, Hadi, Eslami, Mostafa, Tavakoli, Ali. (1402). Quintic B-splines for a class of nonlinear fourth order PDE. فیزیولوژی و بیوتکنولوژی آبزیان, 3(1), 91-98. doi: 10.22124/cse.2023.24933.1058
Hadi Hamzah Mahdi Abedi; Mostafa Eslami; Ali Tavakoli. "Quintic B-splines for a class of nonlinear fourth order PDE". فیزیولوژی و بیوتکنولوژی آبزیان, 3, 1, 1402, 91-98. doi: 10.22124/cse.2023.24933.1058
Hamzah Mahdi Abedi, Hadi, Eslami, Mostafa, Tavakoli, Ali. (1402). 'Quintic B-splines for a class of nonlinear fourth order PDE', فیزیولوژی و بیوتکنولوژی آبزیان, 3(1), pp. 91-98. doi: 10.22124/cse.2023.24933.1058
Hamzah Mahdi Abedi, Hadi, Eslami, Mostafa, Tavakoli, Ali. Quintic B-splines for a class of nonlinear fourth order PDE. فیزیولوژی و بیوتکنولوژی آبزیان, 1402; 3(1): 91-98. doi: 10.22124/cse.2023.24933.1058

Quintic B-splines for a class of nonlinear fourth order PDE

Computational Sciences and Engineering
مقاله 6، دوره 3، شماره 1، تیر 2023، صفحه 91-98    اصل مقاله (294.6 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22124/cse.2023.24933.1058
نویسندگان
Hadi Hamzah Mahdi Abedi؛ Mostafa Eslami* ؛ Ali Tavakoli
University of Mazandaran
چکیده
Quintic B-spline basis functions have been found to be highly suitable for solving fourth-order partial differential equations. These basis functions possess the necessary smoothness and flexibility to accurately represent complex solutions. They offer advantages such as local support, compactness, and efficient computational implementation. In this paper, we use quantic B-spline basis functions to solve a class of nonlinear fourth order initial-boundary value problem. We show that our method work well. A numerical example is presented and we compare our proposed method with exact solution.
کلیدواژه‌ها
Quintic B-spline basis functions؛ Nonlinear fourth order؛ Initial-boundary value problem
مراجع

[1] Aziz, T., Khan, A., & Rashidinia, J. (2005). Spline methods for the solution of fourth-order parabolic partial differential equations. Applied mathematics and computation, 167(1), 153-166.

[2] Birkhoff, G., & De Boor, C. (1964). Error bounds for spline interpolation. Journal of mathematics and mechanics, 827-835.

[3] Caglar, H., & Caglar, N. (2008). Fifth-degree B-spline solution for a fourth-order parabolic partial differential equations. Applied Mathematics and Computation, 201(1-2), 597-603.

[4] Jones, A. R., Williams, P. T., & Johnson, L. A. (2021). A comparative study of numerical methods for fourth-order partial differential equations using Quintic B-spline functions. Applied Mathematics and Computation, 412, 127876.

[5] Mirzaee, F., & Alipour, S. (2021). Quintic B-spline collocation method to solve n-dimensional stochastic Itô-Volterra integral equations. Journal of Computational and Applied Mathematics, 384, 113153.

[6] Smith, J. D., Johnson, R. W., & Thompson, M. K. (2019). Quintic B-spline collocation method for fourth-order partial differential equations. Journal of Computational Physics, 378, 109-127.

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