My work. involved computational modeling and simulations of quark-antiquark interactions (Theoretical High Energy Physics). Specifically, Using anew method that is called matrix Numerov method to study the so-called Spectra of the Quarkonium, which discusses the heavy mesons and studying some properties of bottomonium as an example of heavy mesons. properties. In addition to that, investigating the new numerical method, which are frequently used in the literature. I have independently written all my research codes in Mathematica,