The Radial Basis Function Approximation Method for Solving Bratu-Type Equations

HONG Wen-qiang; XU Ji-qing; XU Xi-bin; ZHANG Chun; ZHOU Shi-liang

doi:10.3879/j.issn.1000-0887.2016.06.007

Volume 37 Issue 6

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Article Navigation > Applied Mathematics and Mechanics > 2016 > 37(6): 617-625

HONG Wen-qiang, XU Ji-qing, XU Xi-bin, ZHANG Chun, ZHOU Shi-liang. The Radial Basis Function Approximation Method for Solving Bratu-Type Equations[J]. Applied Mathematics and Mechanics, 2016, 37(6): 617-625. doi: 10.3879/j.issn.1000-0887.2016.06.007

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The Radial Basis Function Approximation Method for Solving Bratu-Type Equations

doi: 10.3879/j.issn.1000-0887.2016.06.007

¹School of River & Ocean Engineering, Chongqing Jiaotong University,Chongqing 400074, P.R.China;²National Engineering Research Center for Inland Waterway Regulation;Key Laboratory of Hydraulic & Waterway Engineering of the Ministry of Education, Chongqing Jiaotong University, Chongqing 400074, P.R.China;³Chongqing Jianzhu College, Chongqing 400072, P.R.China

Funds: The National Natural Science Foundation of China，The National Basic Research Program of China (973 Program)

Received Date: 2015-12-24
Rev Recd Date: 2016-02-15
Publish Date: 2016-06-15

Abstract

Abstract

Based on the powerful approximation capability of the radial basis function for almost all kinds of functions, and with reference to the interpolation method for elasto-plastic mechanics, the radial basis function expression of the interpolation combining displacement, velocity and acceleration was put forward. Then the MATLAB software was used for computer programming to successfully solve the strongly nonlinear Bratu-type equation, with the corresponding relative errors given and discussed. The analysis of several typical examples was conducted, where the present calculated results were compared with some of the existing numerical results as well as the exact solutions. The comparison shows the feasibility and high accuracy of the present method, which makes a new way of solving the strongly nonlinear Bratu-type equations.
- radial basis function,
- Bratu-type equation,
- strong nonlinearity,
- numerical solution

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References(24)

References

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