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.
Mohsen Didgar, Alireza Vahidi, Jafar Biazar. (2019) Application of Taylor Expansion for Fredholm Integral Equations of the First Kind, Punjab University Journal of Mathematics, Volume 51, Issue 5.
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