چکیده (انگلیسی):

In this paper, we try to study the numerical methods for solving integral equations from a new perspective—machine learning method. By means of the idea of kernel "-support vector regression machine ("-SVR), we construct an optimization modeling for a class of Volterra-Fredholm integral equations and propose a novel numerical method for solving them. The proposed method has a certain versatility and can be used to solve some other kinds of integral equations. In order to verify the effectiveness of the proposed method, we perform a series of comparative experiments with six specific Volterra-Fredholm integral equations and a method proposed in [Wang et al. (2014) Least squares approximation method for the solution of Volterra-Fredholm integral equations, Journal of Computational and Applied Mathematics]. Experimental results show that the proposed method has a good approximation property