Application of variable interchange method for solution of two-dimensional Burgers’ equations

Abstract

In this paper, the change-of-variable method introduced by Boadways [1] is presented for solving a two-dimensional Burgers’ equation. The results are compared with those obtained earlier by other authors [3, 6, 9].

Keywords

• Burger’s equations

Kaynakça

1. J.D. Boadway, Transformation of elliptic partial differential equations for solving two-dimensional boundary problems in fluid flow, Int. Numer. Meth. Engng. 10 (1976) 527.
2. C.A.J. Fletcher, Generating exact solutions of two-dimensional Burgers’ equation, Int. J. Numer. Meth. Fluids 3 (1983) 213-216.
3. P.C. Jain, D.N. Holla, Numerical solution of coupled Burgers’ equations, Int. J. Numer. Meth. Eng. 12 (1978)213-222.
4. O. Goyon, Multilevel schemes for solving unsteady equations, Int. J. Numer. Meth. Fluids 22 (1996) 937-959.
5. F.W. Wubs, E.D. de Goede, An explicit-implicit method for class of time-dependent partial differential equations, App. Numer. Math. 9 (1992) 157-181.
6. A.R. Bahadır, A fully implicit finite-difference scheme for two-dimensional Burgers’ equations, Applied Mathematics and Computataion, 137 (2003) 131-137.
7. S.M. El-Sayed, D. Kaya, On the numerical solution of the system of two-dimensional Burgers’ equations by the decomposition method, Applied mathematics and Computation, 158 (2004) 101-109.
8. H. Zhu, H. Shu, M. Ding, Numerical solutions of two-dimensional Burgers’ equations by discrete Adomian decomposition method, Computers and Mathematics with Applications, 60 (2010) 840-848.

9. V.K. Srivastava, M. Tamsir, U. Bhardwaj, Y. Sanyasiraju, Crank-Nicolson scheme for numerical solutions of two-dimensional coupled Burges’ equations, International Journal of Scientific and Engineering Research, 2(2011) 1-7.
10. V. Gülkaç, Numerical solution of two-dimensional Schrödinger equation by Boadway transformation, International Journal of Computer Mathematics, 80 (2003) 1543-1548.
11. T. Öziş, V. Gülkaç, Application of variable interchange method for solution of two-dimensional fusion problem with convective boundary conditions, Numerical Heat Transfer, Part A, 44 (2008) 85-95.
12. V. Gülkaç, T. Öziş, Treatment of two-dimensional moving boundary problem by Boadway’s transformation, Bull. Cal. Math. Soc. 88 (1996) 253-260.