In this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those methods is produced. Finally, for more explanation, an algorithm is proposed and applied for testing examples to illustrate the effectiveness of the new technique.
Receipt date:10/8/2019 acceptance date:18/12/2019 Publication date:31/12/2021
This work is licensed under a Creative Commons Attribution 4.0 International License.
This research is concerned with the concept of identity in general "Overall definition" and is not exposed to the classifications of identity or concepts that deal with their types and classifications, only the concept in terms of the initial picture as well as the views of thinkers on the proof of
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In the purposes of faith and destiny
Media theories and studies have provided many diligences on the concept of social media and the circle of influence, including the theory of social marketing which deals with how to promote ideas espoused by the elite in a society to become a recognized social value. The emergence of social networks provided a revolutionary breakthrough, taking the media to unprecedented horizons; and giving its users great opportunities to influence and move across borders without restrictions and censorship, except in a relatively limited manner.
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