Numerical solution of Burgers' equation with high order splitting methods

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:291

Article

Seydaoglu, M.^1,3  Erdogan, U.²  Ozis, T.³ 

[1] Mus Alparslan Univ, Fac Art & Sci, Dept Math, TR-49100 Mus, Turkey

[2] Usak Univ, Fac Art & Sci, Dept Math, TR-64200 Usak, Turkey

[3] Ege Univ, Fac Sci, Dept Math, TR-35100 Izmir, Turkey

关键词: Burgers' equation;    Splitting methods;    Extrapolation methods;    Complex coefficients;   

DOI  :  10.1016/j.cam.2015.04.021

来源: Elsevier

【 摘 要 】

In this work, high order splitting methods have been used for calculating the numerical solutions of Burgers' equation in one space dimension with periodic, Dirichlet, Neumann and Robin boundary conditions. However, splitting methods with real coefficients of order higher than two necessarily have negative coefficients and cannot be used for time-irreversible systems, such as Burgers' equations, due to the time-irreversibility of the Laplacian operator. Therefore, the splitting methods with complex coefficients and extrapolation methods with real and positive coefficients have been employed. If we consider the system as the perturbation of an exactly solvable problem (or one that can be easily approximated numerically), it is possible to employ highly efficient methods to approximate Burgers' equation. The numerical results show that both the methods with complex time steps having one set of coefficients real and positive, say a(i) is an element of R+ and b(i) is an element of C+, and high order extrapolation methods derived from a lower order splitting method produce very accurate solutions of Burgers' equation. (C) 2015 Published by Elsevier B.V.

【 授权许可】

Free