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Kadalbajoo, Mohan. K.; Awasthi, A.

A numerical method based on Crank-Nicolson scheme for Burgers’ equation. (English) Zbl 1112.65081

Appl. Math. Comput. 182, No. 2, 1430-1442 (2006).
The authors present a solution based on Crank-Nicolson finite difference method for one-dimensional Burgers’ equation. The Burgers equation arises frequently in mathematical modeling of problems in fluid dynamics. The Hopf-Cole transformation is used to linearize the Burgers’ equation, the resulting heat equation is discretized by using the Crank-Nicolson finite difference scheme. This method is shown to be unconditionally stable and second order accurate in space and time. Numerical results obtained by the present method are compared with exact solution for different values of the Reynolds number.
Reviewer: Vit Dolejsi (Praha)

Cited in 44 Documents

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76M20 Finite difference methods applied to problems in fluid mechanics
35Q53 KdV equations (Korteweg-de Vries equations)
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

Keywords:

Burgers equation; Reynolds number; Hopf-Cole transformation; Crank-Nicolson finite difference method; stability; numerical results
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\textit{Mohan. K. Kadalbajoo} and \textit{A. Awasthi}, Appl. Math. Comput. 182, No. 2, 1430--1442 (2006; Zbl 1112.65081)
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