Journal of Applied Mathematics

HAM-Based Adaptive Multiscale Meshless Method for Burgers Equation

Shu-Li Mei

Full-text: Open access

Abstract

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.

Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 248246, 10 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394808120

Digital Object Identifier
doi:10.1155/2013/248246

Mathematical Reviews number (MathSciNet)
MR3096068

Zentralblatt MATH identifier
06950581

Citation

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


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