Numerical solution of Burgers' equation with high order splitting methods

Küçük Resim Yok

Tarih

2016

Dergi Başlığı

Dergi ISSN

Cilt Başlığı

Yayıncı

Elsevier Science Bv

Erişim Hakkı

info:eu-repo/semantics/closedAccess

Özet

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.

Açıklama

Anahtar Kelimeler

Burgers' equation, Splitting methods, Extrapolation methods, Complex coefficients

Kaynak

Journal of Computational and Applied Mathematics

WoS Q Değeri

Q1

Scopus Q Değeri

N/A

Cilt

291

Sayı

Künye