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| The Sinc-Galerkin methods of the Burgers' equation based on the Hopf-Cole transformation |
| Received:October 24, 2018 Revised:December 19, 2018 |
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| DOI：10.7511/jslx20181024001 |
| KeyWord:Burgers's equation Sinc-Galerkin methods Hopf-Cole transformation Second boundary condition |
| Author | Institution |
| 杨梅 |
西安理工大学 理学院, 西安 |
| 赵凤群 |
西安理工大学 理学院, 西安 |
| 郭冲 |
西安理工大学 理学院, 西安 |
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| Abstract: |
| In this paper,the Sinc-Galerkin method is used to solve the initial boundary value problem of the Burgers equation.Firstly,the Hopf-Cole transform is used to transform the second-order nonlinear Burgers equation into a second-order linear equation,while the first type of boundary condition is changed into the second type of boundary condition.Then the time derivative is discretized in θ-weighted scheme,and the spatial derivative is discretized by the Sinc-Galerkin method.For the second type of boundary condition,the basis functions are introduced at the ends based on Hermite interpolation method.Finally,the validity and exponential convergence of the Sinc-Galerkin method is verified by numerical examples.A comparison between the numerical solution and the exact solution shows that numerical scheme constructed in this paper has high accuracy,and can effectively capture physical phenomena such as shock waves. |
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