Application of Taylor Expansion for Fredholm Integral Equations of the First Kind

Abstract

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 νth-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 ν. 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 ν, the derived νth-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.