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Combinations of the Boundary Knot Method with Analogy Equation Method for Nonlinear Problems

K.H. Zheng1, H.W. Ma2,3
Tianxiang Road 289#, College of Water Conservancy and Ecological Engineering, Nanchang Institute of Technology, Nanchang 330099, China
South University Ave. 88#, College of Civil Science and Engineering, Yangzhou University, Yangzhou 225009 China
Corresponding to: hhu2000@163.com

Computer Modeling in Engineering & Sciences 2012, 87(3), 225-238. https://doi.org/10.3970/cmes.2012.087.225

Abstract

Based on the analogy equation method and method of particular solutions, we propose a combined boundary knot method (CBKM) for solving nonlinear problems in this paper. The principle of the CBKM lies in that the analogy equation method is used to convert the nonlinear governing equation into a corresponding linear inhomogeneous one under the same boundary conditions. Then the method of particular solutions and boundary knot method are, respectively, used to construct the particular and homogeneous solutions for the newly-introduced inhomogeneous equation. Finally, the field function and its derivatives involved in the nonlinear governing equation are expressed via the unknown coefficients, which are established by collocating the equations at discrete knots on the physical domain. A classical nonlinear problem, among numerous examples, is chosen to validate the convergence, stability and accuracy of the proposed method.

Keywords

Boundary knot method, analogy equation method, nonlinear, radial basis function.

Cite This Article

Zheng, K., Ma, H. (2012). Combinations of the Boundary Knot Method with Analogy Equation Method for Nonlinear Problems. CMES-Computer Modeling in Engineering & Sciences, 87(3), 225–238.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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