In this paper, the Ritz-Galerkin method in Bernstein polynomial basis is applied for solving the nonlinear problem of the magnetohydrodynamic (MHD) flow of third grade fluid between the two plates. The properties of the Bernstein  polynomials together with the Ritz-Galerkin method are used to reduce the solution of the MHD Couette flow of non-Newtonian fluid in a porous medium to the solution o...

in this paper, the stability characteristics of single-walled carbon nanotubes (swcnts) under the action of axial load are investigated. to this end, a nonlocal flügge shell model is developed to accommodate the small length scale effects. the analytical rayleigh-ritz method with beam functions is applied to the variational statement derived from the flügge-type buckling equations. molecular dy...

Pollution has become a very serious threat to our environment. Monitoring pollution is the rst step toward planning to save the environment. The use of dierential equations, monitoring pollution has become possible. In this paper, a Ritz-collocation method is introduced to solve non-linear oscillatory systems such as modelling the pollution of a system of lakes. The method is based upon Bernoul...

in this study, the free vibration of partially fluid-filled laminated composite circular cylindrical shell with arbitrary boundary conditions has been investigated by using rayleigh-ritz method. the analysis has been carried out with strain-displacement relations based on love’s thin shell theory and the contained fluid is assumed irrotational, incompressible and inviscid. after determining the...

In this paper, we apply He’s semi-inverse method to establish a variational theory for the Boussinesq system. Based on this formulation, a solitary solution can be easily obtained using Ritz method. Moreover, the results are also compared with He’s homotopy perturbation method, Liao’s homotopy analysis method and homotopy padémethod. The results reveal that the proposed method is very effective...

The block preconditioned steepest descent iteration is an iterative eigensolver for subspace eigenvalue and eigenvector computations. An important area of application of the method is the approximate solution of mesh eigenproblems for self-adjoint and elliptic partial differential operators. The subspace iteration allows to compute some of the smallest eigenvalues together with the associated i...

We analyze the Ritz–Galerkin method for symmetric eigenvalue problems and prove a priori eigenvalue error estimates. For a simple eigenvalue, we prove an error estimate that depends mainly on the approximability of the corresponding eigenfunction and provide explicit values for all constants. For a multiple eigenvalue we prove, in addition, apparently the first truly a priori error estimates th...

The goal of this paper is to increase our understanding of harmonic Rayleigh– Ritz for real symmetric matrices. We do this by discussing different, though related topics: a priori error analysis, a posteriori error analysis, a comparison with refined Rayleigh–Ritz and the selection of a suitable harmonic Ritz vector.

in this paper for a given prescribed ritz values that satisfy in the some special conditions, we nd a symmetric nonnegative matrix, such that the given set be its ritz values.