An approximate solution for a mixed linear Volterra–Fredholm integral equation

In this work, a method called the Taylor expansion method is used to solve a mixed linear Volterra–Fredholm integral equation of the second kind. A strict theory is established. The advantages of this method lie in that, on the one hand, the exact solution is obtained if the true solution is a polynomial, and on the other hand, if the true solution is not a polynomial, an approximate solution with high accuracy called an ε -approximate solution will be obtained by taking several terms. In short, our method is fast and efficient.