کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6892292 1445353 2017 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A new algorithm based on Lucas polynomials for approximate solution of 1D and 2D nonlinear generalized Benjamin-Bona-Mahony-Burgers equation
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر علوم کامپیوتر (عمومی)
پیش نمایش صفحه اول مقاله
A new algorithm based on Lucas polynomials for approximate solution of 1D and 2D nonlinear generalized Benjamin-Bona-Mahony-Burgers equation
چکیده انگلیسی
In this paper, a new method based on hybridization of Lucas and Fibonacci polynomials is developed for approximate solutions of 1D and 2D nonlinear generalized Benjamin-Bona-Mahony-Burgers equations. Firstly time discretization is made by using finite difference approaches. After that unknown function and its derivatives are expanded to Lucas series. Based on these series expansion, differentiation matrices are derived by utilizing Fibonacci polynomials. By doing so, the solution of the mentioned equations is reduced to the solution of an algebraic system of equations. By solving this system of equations the Lucas series coefficients are obtained. Then substituting these coefficients into Lucas series expansion approximate solutions can be constructed successively. The main goal of this paper is to indicate that Lucas polynomial based method is appropriate for 1D and 2D nonlinear problems. Efficiency and performance of the proposed method are judged on six test problems which consists of the 1D and 2D version of mentioned equation by calculating L2 and L∞ error norms. Feasibility of the method is verified by obtained accurate results.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computers & Mathematics with Applications - Volume 74, Issue 12, 15 December 2017, Pages 3042-3057
نویسندگان
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