We proposed Relativistic Quantum Electrodynamics in matters under strong external fields obeying to Finite Schwinger Dyson Formalism. The original Schwinger-Dyson formalism (SD formalism) is generalized for the application to atoms, molecules and electron matters under external fields. Because the generalized formalism has some important differences from original SD formalism widely used in ele...

An analogue of Kolmogorov’s superconvergent perturbation theory in classical mechanics is constructed for self adjoint operators. It is different from the usual Rayleigh–Schrödinger perturbation theory and yields expansions for eigenvalues and eigenvectors in terms of functions of the perturbation parameter. PACS Code: 03.65.-w, 31.15+q, 02.30.Mv, 02.90.+p

Some multi degree-of-freedom dynamical systems exhibit a response that contain fast and slow variables. An example of such systems is a multibody system with rigid and deformable bodies. Standard numerical integration of the resultant equations of motion must adjust the time step according to the frequency of the fastest variable. As a result, the computation time is sacrificed. The singular pe...

In this paper, He’s homotopy perturbation method (HPM) is applied for solving linear programming (LP) problems. This paper shows that some recent findings about this topic cannot be applied for all cases. Furthermore, we provide the correct application of HPM for LP problems. The proposed method has a simple and graceful structure. Finally, a numerical example is displayed to illustrate the pro...

analyzing the nonlinear vibration of beams is one of the important issues in structural engineering. according to this, an impressive analytical method which is called modified iteration perturbation method (mipm) is used to obtain the behavior and frequency of a cantilever beam with geometric nonlinear. this new method is combined by the mickens and iteration methods. moreover, this method don...

The Computational Singular Perturbation (CSP) method, developed by Lam and Goussis [Twenty-Second Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1988, pp. 931–941], is a commonly-used method for finding approximations of slow manifolds in systems of ordinary differential equations (ODEs) with multiple time scales. The validity of the CSP method was established fo...

Abstract. Renormalization group method is one of the most powerful tool to obtain approximate solutions to differential equations. We apply the renormalization group method to Hamiltonian systems whose integrable parts linearly depend on action variables. We show that the renormalization group method gives the same approximate solutions as canonical perturbation theory up to the second order of...

The homotopy perturbation method is extremely accessible to non-mathematicians and engineers. The method decomposes a complex problem under study into a series of simple problems that are easy to be solved. This note gives an elementary introduction to the basic solution procedure of the homotopy perturbation method. Particular attention is paid to constructing a suitable homotopy equation. Thi...