کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1722031 | 1014708 | 2015 | 9 صفحه PDF | دانلود رایگان |
In this paper, the multi-scale Runge-Kutta_Galerkin method is developed for solving the evolution equations, with the spatial variables of the equations being discretized by the multi-scale Galerkin method based on the multi-scale orthogonal bases in Hm0(a,b) and then the classical fourth order explicit Runge-Kutta method being applied to solve the resulting initial problem of the ordinary differential equations for the coefficients of the approximate solution. The proposed numerical scheme is validated by applications to the Burgers equation (nonlinear convection-diffusion problem), the KdV equation (single solitary and 2-solitary wave problems) and the KdV-Burgers equation, where analytical solutions are available for estimating the errors. Numerical results show that using the algorithm we can solve these equations stably without the need for extra stabilization processes and obtain accurate solutions that agree very well with the corresponding exact solutions in all cases.
Journal: Journal of Hydrodynamics, Ser. B - Volume 27, Issue 3, June 2015, Pages 443-451