Approximate Solution of Linear Volterra-Fredholm Integral Equations and Systems of Volterra-Fredholm Integral Equations Using Taylor Expansion Method

In this study, a new application of Taylor expansion is considered to estimate the solution of Volterra-Fredholm integral equations (VFIEs) and systems of Volterra-Fredholm integral equations (SVFIEs). Our proposed method is based upon utilizing the nth-order Taylor polynomial of unknown function at an arbitrary point and employing integration method to convert VFIEs into a system of linear equations with respect to unknown function and its derivatives. An approximate solution can be easily determined by solving the obtained system. Furthermore, this method leads always to the exact solution if the exact solution is a polynomial function of degree up to n. Also, an error analysis is given. In addition, some problems are provided to demonstrate the validity and applicability of the proposed method.