Taylor polynomial method and error estimation for a kind of mixed Volterra–Fredholm integral equations

摘要

In this paper, an efficient numerical method of Taylor polynomial method is developed to solve the Volterra–Fredholm integral equations. This method is based on first taking truncated Taylor series of the functions in equation and then substituting them into the given equation, thereby the equation reduces to a matrix equation, finally, we can solve the unknown Taylor coefficients and obtained the approximation of solution. Error estimation and illustrative examples are included to demonstrate the validity and applicability of the method.