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In this paper, a numerical solution of the coupled Burgers' equations based on septic Bspline collocation method is presented. The scheme is based on the Crank-Nicolson formulation for time integration and septic B-spline functions for space integration. The method has been showed unconditionally stable by using Von-Neumann technique. The efficiency of this method is demonstrated by applying two test problems. The obtained numerical results are found in a good agreement with the exact solution. This method is efficient, powerful, and economical. It can also applicable to other linear and nonlinear partial differential equations.

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