Journal of Applied Mathematics
- J. Appl. Math.
- Volume 2013 (2013), Article ID 248246, 10 pages.
HAM-Based Adaptive Multiscale Meshless Method for Burgers Equation
Based on the multilevel interpolation theory, we constructed a meshless adaptive multiscale interpolation operator (MAMIO) with the radial basis function. Using this operator, any nonlinear partial differential equations such as Burgers equation can be discretized adaptively in physical spaces as a nonlinear matrix ordinary differential equation. In order to obtain the analytical solution of the system of ODEs, the homotopy analysis method (HAM) proposed by Shijun Liao was developed to solve the system of ODEs by combining the precise integration method (PIM) which can be employed to get the analytical solution of linear system of ODEs. The numerical experiences show that HAM is not sensitive to the time step, and so the arithmetic error is mainly derived from the discrete in physical space.
J. Appl. Math., Volume 2013 (2013), Article ID 248246, 10 pages.
First available in Project Euclid: 14 March 2014
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Mei, Shu-Li. HAM-Based Adaptive Multiscale Meshless Method for Burgers Equation. J. Appl. Math. 2013 (2013), Article ID 248246, 10 pages. doi:10.1155/2013/248246. https://projecteuclid.org/euclid.jam/1394808120