Hybrid spline difference method for the Burgers' equation

Abstract This study developed a high accuracy hybrid spline difference method, and deduced a difference equation that is very similar to finite difference method from the concept of spline difference. As validated by nonlinear Burgers’ equation, the concept of difference made the computational process as simple as the finite difference method, and easy to be implemented. The free parameters α → 1 / 12 and α → 1 / 6 were combined in the concept of spline hybrid, in order to increase the accuracy of the first and second derivatives of space from O ( h 2 ) of finite difference method to the O ( h 4 ) . The accuracy was improved, and the numerical oscillation with the increase in parameter R e was improved greatly.

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