| Wavelet solutions of Burgers’ equation with high Reynolds numbers |
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| 基金项目： | supported by the National Natural Science Foundation of China(Grant Nos.11032006,11072094,and 11121202);the Ph.D.Program Foundation of Ministry of Education of China(Grant No.20100211110022);the National Key Project of Magneto-Constrained Fusion Energy Development Program(Grant No.2013GB110002);the Fundamental Research Funds for the Central Universities(Grant No.lzujbky-2013-1);the Scholarship Award for Excellent Doctoral Student granted by the Lanzhou University |
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| 摘 要： | A wavelet method is proposed to solve the Burgers’equation.Following this method,this nonlinear partial differential equation is first transformed into a system of ordinary differential equations using the modified wavelet Galerkin method recently developed by the authors.Then,the classical fourth-order explicit Runge–Kutta method is employed to solve the resulting system of ordinary differential equations.Such a wavelet-based solution procedure has been justified by solving two test examples:results demonstrate that the proposed method has a much better accuracy and efficiency than many other existing numerical methods,and whose order of convergence can go up to 5.Most importantly,our results also indicate that the present wavelet method can readily deal with those fluid dynamics problems with high Reynolds numbers.
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| 关 键 词： | modified wavelet Galerkin method Runge–Kutta method Burgers' equation high Reynolds number |
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