AbstractThis article scrutinizes the efficacy of analytical mathematical schemes, improved simple equation and exp(-\text{Ψ}(\xi ))-expansion techniques for solving the well-known nonlinear partial differential equations. A longitudinal wave model is used for the description of the dispersion in the circular rod grounded via transverse Poisson’s effect; similarly, the Boussinesq equation is used for extensive wave propagation on the surface of water. Many other such types of equations are also solved with these techniques. Hence, our methods appear easier and faster via symbolic computation.
The calculation of QCD corrections to heavy quark decay rates has progressed steadily in recent years. With the help of specialized techniques, symbolic computation, and a growing base of experience, a wide variety of special cases have been evaluated. These results have been applied to decays such as t → bW, b → s γ, b → u[Formula: see text]ν, and b → c[Formula: see text]ν. PACS Nos.: 12.38.Bx, 13.30.Ce