The results show that the disturbance of a combination of the Eckart potential and trigonometric Manning Rosen potential can change the radial part and the angular part of the wave function. The radial part and the angular part of the wave function are defined as hypergeometry functions and visualized with Matlab 2011. The energy spectrum is also numerically solved using the Matlab software, where the increase in the radial quantum number nr causes the energy to decrease. With the asymptotic iteration method, the energy spectra of the relativistic equations and equations of orbital quantum number l can be obtained, where both are interrelated between quantum numbers. This study is limited to the case of spin symmetry. The relativistic energy is calculated using Matlab 2011. The Dirac equation is solved by using an asymptotic iteration method that can reduce the second order differential equation into a differential equation with substitution variables of hypergeometry type. The combination of the two potentials is substituted into the Dirac equation, then the variables are separated into radial and angular parts. The Dirac equation for Eckart potential and trigonometric Manning Rosen potential with exact spin symmetry is obtained using an asymptotic iteration method. Solution of Dirac equation for Eckart potential and trigonometric Manning Rosen potential using asymptotic iteration method Guidelines for suitable mesh and time step choices are given. Analysis of the discretized model problem supports these numerical results. Numerical results for effects of mesh size, extent, and stretching, time step size, and choice of far-field boundary conditions are presented. The one-dimensional equation considered provides a suitable model for the study of wave propagation in the equations of transonic small disturbance potential flow. The personal computer provides a convenient and useful tool for the development of meshes, algorithms, and boundary conditions needed to provide time accurate solution of these equations. Personal computer study of finite-difference methods for the transonic small disturbance equationĬalculation of unsteady flow phenomena requires careful attention to the numerical treatment of the governing partial differential equations.
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