论文信息 - On a finite difference scheme for Burgers' equation

On a finite difference scheme for Burgers' equation

In this paper we study properties of numerical solutions of Burger's equation. Burgers' equation is reduced to the heat equation on which we apply the Douglas finite difference scheme. The method is shown to be unconditionally stable, fourth order accurate in space and second order accurate in time. Two test problems are used to validate the algorithm. Numerical solutions for various values of viscosity are calculated and it is concluded that the proposed method performs well.

Amit K. Verma | K. Pandey | Lajja Verma

[1] S. Kutluay,et al. Numerical solution of one-dimesional Burgers equation: explicit and exact-explicit finite difference methods , 1999 .

[2] E. Hopf. The partial differential equation ut + uux = μxx , 1950 .

[3] E. N. Aksan,et al. A numerical solution of Burgers' equation , 2004, Appl. Math. Comput..

[4] J. Burgers. A mathematical model illustrating the theory of turbulence , 1948 .

[5] J. Cole. On a quasi-linear parabolic equation occurring in aerodynamics , 1951 .

[6] David J. Evans,et al. The Group Explicit method for the solution of Burger's equation , 1984, Computing.

[7] M. K. Kadalbajoo,et al. A numerical method based on Crank-Nicolson scheme for Burgers' equation , 2006, Appl. Math. Comput..

[8] Poonam Singhal,et al. Numerical solution of Burger's equation , 1993 .

[9] G. Hedstrom,et al. Numerical Solution of Partial Differential Equations , 1966 .

[10] H. Bateman,et al. SOME RECENT RESEARCHES ON THE MOTION OF FLUIDS , 1915 .