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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. [ABSTRACT FROM AUTHOR]

This investigation intends to provide a new application of Taylor expansion approach for solving first kind Fredholm integral equations. The approach is based on employing the vth-degree Taylor polynomial of unknown function at an arbitrary point and integration method such that the first kind Fredholm integral equation is converted into a linear equations system with respect to unknowns and its derivatives up to order v. Solving this system will result in a desired solution. A considerable advantage of the suggested approach is that for such cases when the true solution is a polynomial function of degree at most v, the derived vth-degree approximation is equal to true solution. An error analysis is represented and to verify the effectively and the accuracy of the proposed approach six examples are investigated. [ABSTRACT FROM AUTHOR]