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標題: A Nonlinear Numerical Solution for Burgers' Equation
Burgers 方程的非線性數值解
作者: 蕭智維
Chih-Wei Hsiao
引用: [1] Personal discussion with Y.T. Lin, C.C. Tsai, and Y.T. Shih. [2] W.F. Ames (1992), 'Numerical methods for partial differential equations', 3rd edition, Academic Press. [3] A.R. Bahadır and M. Sağlam (2005), 'A mixed finite difference and boundary element approach to one-dimensional Burgers' equation', Applied Mathematics and Computation 160: 663-673. [4] R. Barrett, M. Berry, T.F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. Van der Vorst (1994), 'Templates for the solution of linear systems: building blocks for iterative methods' 2nd Edition, SIAM, Philadelphia, PA. [5] H. Bateman (1915), 'Some recent researches on the motion of fluids', Monthly Weather Review, vol. 43, issue 4: 163-170. [6] J.D. Faires and R. Burden (2013), 'Numerical Methods', 4th edition, Brooks and Cole. [7] M.H. Gutknecht (2007), 'A brief introduction to Krylov space methods for solving linear systems', Frontiers of Computational Science: 53-62. [8] C.T. Kelley (1995), 'Iterative methods for linear and nonlinear equations', SIAM, Philadelphia, PA. [9] C.T. Kelley, I.G. Kevrekidis, and L. Qiao (2004), 'Newton-Krylov solvers for time-steppers', Cornell University Library. [10] S. Kutluay, A.R. Bahadır, and A. Özdeş (1999), 'Numerical solution of one-dimensional Burgers equation: explicit and exact-explicit finite difference meth-ods', Journal of Computational and Applied Mathematics 103: 251-261. [11] S. Kutluay, A. Esen, and I. Dag (2004), 'Numerical solutions of the Burg-ers' equation by the least-squares quadratic B-spline finite element method', Journal of Computational and Applied Mathematics 167: 21-33. [12] M.B. Abd-el-Malek and S. M.A. El-Mansi (2000), 'Group theoretic methods applied to Burgers' equation', Journal of Computational and Applied Mathe-matics 115: 1-12. [13] K. Pandey, L. Verma, and A.K. Verma (2009), 'On a finite difference scheme for Burgers' equation', Applied Mathematics and Computation 215: 2206-2214. [14] Y. Saad and M.H. Schultz (1986), 'GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems', SIAM Journal on Scientific and Statistical Computing, Vol. 7, No. 3: 856-869. [15] Y.T. Shih (1998), 'Upwind finite element solutions for convection-diffusion problems', Ph. D. Dissertation, University of Maryland, College Park, MD. [16] P.G. Zhang and J.P. Wang (2012), 'A predictor-corrector compact finite dif-ference scheme for Burgers' equation', Applied Mathematics and Computation 219: 892-898. [17] G.Z.Zhao, X.J. Yu, and D. Wu (2010), 'Numerical solution of the Burgers' equation by local discontinuous Galerkin method', Applied Mathematics and Computation 216: 3671-3679.
摘要: In this thesis, we present two discretization methods for solving Burgers' Equa-tion. By using linear methods, we modify the Crank-Nicolson method by replacing unknown non-linear terms of Burgers' Equation with known ones. In non-linear way, we propose Crank-Nicolson with Newton GMRES method to solve Burgers' Equation. And we take some comparisons of results of these two methods. Both methods get good approximations for Burgers' Equation.
本論文呈現兩種解 Burgers 方程的離散方法。在線性方法中,藉由已知項替換Burgers 方程的未知非線性項,修改了 Crank-Nicolson 法。在非線性方法中,我們提出結合 Crank-Nicolson 與牛頓 GMRES 的方法解 Burgers 方程,並且比較兩種方法的結果。兩種方法對於 Burgers 方程都有良好的近似解。
文章公開時間: 2017-07-16
Appears in Collections:應用數學系所



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