We will transform Numerov’s method into a representation of matrix form to solve Schrödinger equation. The validity of the method is tested by applying it to calculate spectra of bottomonium. We compare our results with the experimentally observed masses and theoretically predicted results. The obtained results are found to be in good agreement with the experimental results.

Numerical simulations of the nonlinear acoustic waves for medical applications are performed by using Westervelt equation. In this paper, FDTD has been introduced to solve Westervelt equation. Nonlinear propagation scheme is applied on different biological media where a 1 kpa transducer pressure wave of 1 MHz and interactions with tissues are analyzed. Our results show the importance of considering nonlinear interactions in understanding the behavior of sound waves in biological tissues

A detailed analysis is conducted on the sources of Beauty mesons (B mesons) through the strong decay of ηb(5S), which represents one of the singlet-spin states S-wave bottomonium mesons. That is considered a significant step in understanding the physics behind the strong decay of bottomonium mesons, which is demonstrated to furnish us with a plentiful source of Beauty mesons. Their rare decay is regarded as a gateway to a new realm of physics, commonly called New Physics or Beyond Standard Model. The expected masses for higher bottomonium mesons are determined within the framework of the nonrelativistic quark model, and the recently obtained experimental data exhibit substantial concordance with our findings. Additionally, other theoretical forecasts align with our outcomes. The Quark Pair Creation model is employed to compute the strong decay of the ηb(5S) meson. Moreover, the strong decay branching ratio is determined. Novel findings regarding the partial strong decay widths of the ηb(5S) are obtained, while the total decay width aligns with previous studies. The strong decay width of the B*B* mesonic pairs channel is expected to be the greatest width by the ratio (∼ 56.37 %) concerning the higher scalar ηb(5S) state. Additionally, the Bs*Bs* channel is predicted to have the next-to-dominant width relative to ηb(5S) state.