LS-SVR-based solving Volterra integral equations

In this paper, a novel hybrid method is presented for solving the second kind linear Volterra integral equations. Due to the powerful regression ability of least squares support vector regression (LS-SVR), we approximate the unknown function of integral equations by using LS-SVR in intervals with known numerical solutions. The trapezoid quadrature is used to approximate subsequent integrations in intervals with unknown numerical solutions. The feasibility of the proposed method is examined on some integral equations. Experimental results of comparison with analytic and repeated modified trapezoid quadrature method's solutions show that the proposed algorithm could reach a very high accuracy. The proposed algorithm could be a good tool for solving the second kind linear Volterra integral equations.