Numerical simulation of Volterra–Fredholm integral equations using least squares support vector regression

In this paper, a new method based on least squares support vector regression (LS-SVR) is presented as a numerical method for solving linear and nonlinear Volterra–Fredholm integral equations. To minimize the residual function associated with the integral equation, the resulting optimization quadratic problem is written as a linear system by introducing some dual variables. Legendre polynomials are used as the kernel of LS-SVR. Finally, the proposed LS-SVR method is applied to some test problems, and the numerical results are compared with some existing methods, representing the accuracy and efficiency of the method.