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A numerical method based on Crank-Nicolson scheme for Burgers’ equation. (English) Zbl 1112.65081
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.
MSC:
65M06Finite difference methods (IVP of PDE)
76M20Finite difference methods (fluid mechanics)
35Q53KdV-like (Korteweg-de Vries) equations
65M12Stability and convergence of numerical methods (IVP of PDE)