Direct simulation methods of Electron Paramagnetic Resonance (EPR) spectra are an alternative to standard eigenfunction-based approaches. Both methods can be employed to find numerical solutions of the Stochastic Liouville Equation (SLE) in order to compute spectral lineshapes. It can be shown rigorously that the domain of validity of eigenfunction expansion solutions of the SLE covers only a l...

An alternative method for deriving water wave dispersion relations and evolution equations is to use a weak formulation. The free-surface displacement η is written as an eigenfunction expansion,

We extend the Adomian's decomposition method to work for the general eigenvalue problems, in addition to the existing applications of the method to boundary and initial value problems with nonlinearity. We develop the Hamiltonian inverse iteration method which will provide the ground state eigenvalue and the explicit form eigenfunction within a few iterations. The method for finding the excited...

An effective numerical method based on Legendre polynomials is proposed for the solution of a class of variational problems with suitable boundary conditions. The Ritz spectral method is used for finding the approximate solution of the problem. By utilizing the Ritz method, the given nonlinear variational problem reduces to the problem of solving a system of algebraic equations. The advantage o...

In the presented paper, the governing equations of a vibratory beam with moderately large deflection are derived using the first order shear deformation theory. The beam is homogenous, isotropic and it is subjected to the dynamic transverse and axial loads. The kinematic of the problem is according to the Von-Karman strain-displacement relations and the Hook's law is used as the constitutive eq...