In this investigation Rayleigh-Ritz variational method has been applied to determine the least natural frequency coefficient for the title problem. Classical plate theory assumptions have been used to calculate strain energy and kinetic energy. Coordinate functions are combination of polynomials which satisfy boundary conditions at the outer boundary and trigonometric terms. In the second part ...

We present some new error estimates for the eigenvalues and eigenfunctions obtained by the Rayleigh-Ritz method, the common variational method to solve eigenproblems. The errors are bounded in terms of the error of the best approximation of the eigenfunction under consideration by functions in the ansatz space. In contrast to the classical theory, the approximation error of eigenfunctions other...

We consider a parallel method for solving generalized eigenvalue problems that arise from molecular orbital calculation of the biochemistry application. Our focus is to develop scalable parallel implementations of the method that achieves high performance on multi-core clusters. In a Rayleigh-Ritz type method using a contour integral (CIRR method), the computation at each contour involves linea...

The Rayleigh–Ritz (rr) method is well known as a means of minimizing energy functionals. Despite this, the technique most often employed in practice for minimizing a functional is the numerical solution of the Euler–Lagrange (el) equations derived from the energy functional by variational minimization. In this article we employ the rr method specifically to determine the equilibrium shape of a ...

In this work, we discuss a one dimensional inverse problem for the heat equation where unknown functions are solely time-dependent lower order coefficient and multiplicative source term. We use as data two integral overdetermination conditions along with initial Dirichlet boundary conditions. first step, term is eliminated by applying transformation converted to an equivalent of determining con...