A Method of Solving a Class of Nonlinear Integral Equation in the Reproducing Kernel Space

In the study, we will give a method of solving the solution for the nonlinear Volterra-Fredholm integral equation in the reproducing kernel space W(D). The problem on solving the solution of the nonlinear Volterra-Fredholm integral equation is transformed into the problem of solving system of linear equations. The approximate solution converges to exact solution of the nonlinear Volterra-Fredholm integral equation in the sense of . but also in the sense of . C. In addition, the error of the approximate solution is monotone deceasing and high convergence order in the sense of. Numerical experiments illustrate the method is efficient.