| 45 | 0 | 80 |
| 下载次数 | 被引频次 | 阅读次数 |
使用一种改进的三次B样条配置法求解Benjamin-Bona-Mahony-Burgers(BBMB)方程.通过限制标准三次B样条高阶导数，利用Crank-Nicolson格式将时间离散化，并采用线性化过程处理非线性项，结合空间上改进的三次B样条函数离散化，实现了对BBMB方程的高效数值求解.通过Von-Neumann稳定性分析，验证了该方法的稳定性.数值实验表明，该方法在空间上达到六阶收敛精度.
Abstract：In this paper, an improved cubic B-spline configuration method was used to solve the Benjamin-Bona-Mahony-Burgers(BBMB) equation. By limiting the high order derivatives of standard cubic B-splines, the time was discretized by Crank-Nicolson scheme, and the nonlinear terms were treated by linearization process. Combined with the spatially improved cubic B-spline function discretization, the efficient numerical solution of the BBMB equation was realized. The stability of the proposed method was verified by Von-Neumann stability analysis. Numerical experiments showed that the proposed method achieves the sixth order convergence accuracy in space.
[1] BRUZóN M,GANDARIAS M.Some travelling wave solutions for a generalized Benjamin-Bona-Mahony-Burgers equation by using MAXIMA program[C]//2011 International Conference on Software Engineering(ICSE).Cambridge:WSEAS,2011:138-143.
[2] RAUPP M A.Galerkin methods applied to the Benjamin-Bona-Mahony equation[J].Bol Da Sociedade Bras De Matemática Bull Math Soc,1975,6(1):65-77.
[3] LAI S Y,LV X M,SHUAI M Y.The Jacobi elliptic function solutions to a generalized Benjamin-Bona-Mahony equation[J].Math Comput Model,2009,49(1/2):369-378.
[4] AL-KHALED K,MOMANI S,ALAWNEH A.Approximate wave solutions for generalized Benjamin-Bona-Mahony-Burgers equations[J].Appl Math Comput,2005,171(1):281-292.
[5] GHEORGHIU C I.Stable spectral collocation solutions to a class of Benjamin Bona Mahony initial value problems[J].Appl Math Comput,2016,273:1090-1099.
[6] ZAREBNIA M,PARVAZ R.Error analysis of the numerical solution of the Benjamin-Bona-Mahony-Burgers equation[J].B Soc Paran Mat,2019,38(3):177-191.
[7] SALIH H.Solution BBM-Burger equation via quartic trigonometric B-spline approach[J].J Phys:Conf Ser,2021,1879(2):022109.
[8] KUNG J,ROTA G C.A practical guide to splines[J].Adv Math,1979,32(1):81.
[9] VARGA R S.On diagonal dominance arguments for bounding ‖A-1‖∞[J].Linear Algebra Appl,1976,14(3):211-217.
[10] GARDNER L R T,GARDNER G A,DAG I.A B-spline finite element method for the regularized long wave equation[J].Commun Numer Meth Eng,1995,11(1):59-68.
[11] KUTLUAY S,ESEN A.A finite difference solution of the regularized long-wave equation[J].Math Probl Eng,2006,2006(1):085743.
[12] ARORA G,MITTAL R C,SINGH B K.Numerical solution of BBM-Burger equation with quartic B-spline collocation method[J].J Eng Sci Technol,2014,9:104-116.
[13] ZAREBNIA M,PARVAZ R.On the numerical treatment and analysis of Benjamin-Bona-Mahony-Burgers equation[J].Appl Math Comput,2016,284:79-88.
[14] SHALLU,KUKREJA V K.Numerical treatment of Benjamin-Bona-Mahony-Burgers equation with fourth-order improvised B-spline collocation method[J].J Ocean Eng Sci,2022,7(2):99-111.
[15] GHASEMI M.An efficient algorithm based on extrapolation for the solution of nonlinear parabolic equations[J].Int J Nonlinear Sci Numer Simul,2018,19(1):37-51.
[16] MOHAMMADI R.B-spline collocation algorithm for numerical solution of the generalized Burger's-Huxley equation[J].Numer Meth Partial Differ Equ,2013,29(4):1173-1191.
[17] CHEN Y,LI B,ZHANG H Q.Exact solutions for two nonlinear wave equations with nonlinear terms of any order[J].Commun Nonlinear Sci Numer Simul,2005,10(2):133-138.
基本信息:
DOI：10.19926/j.cnki.issn.1674-232X.2023.05.262
中图分类号:O241.7
引用信息:
[1]胡志涛,全赛君,岳宏杰等.解BBMB方程的改进三次B样条配置法[J].杭州师范大学学报(自然科学版),2025,24(01):88-97+112.DOI:10.19926/j.cnki.issn.1674-232X.2023.05.262.
基金信息:
国家自然科学基金项目(11471092)