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
 Citation: 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.

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

##### doi: 10.3879/j.issn.1000-0887.2016.06.007
Funds:  The National Natural Science Foundation of China，The National Basic Research Program of China (973 Program)
• Rev Recd Date: 2016-02-15
• Publish Date: 2016-06-15
• 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.
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