Hybrid spline difference method for the Burgers’ equation

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摘要

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(h2) of finite difference method to the O(h4). The accuracy was improved, and the numerical oscillation with the increase in parameter Re was improved greatly.

论文关键词:Hybrid spline difference method,Burgers’ equation,Parametric spline,Finite difference method,High accuracy

论文评审过程:Available online 31 July 2012.

论文官网地址:https://doi.org/10.1016/j.amc.2012.07.007