Microvibrations at frequencies between 1 and 1000 Hz generated by on-board equipment can propagate through a satellite's structure and hence signiicantly reduce the performance of sensitive payloads. This paper describes a Lagrange-Rayleigh-Ritz method for developing models suitable for the design of active control schemes. Here Loop Transfer Recovery based controller design methods are employe...

Multigrid algorithms are the method of choice for solving large Ritz-Galerkin systems for elliptic boundary value problems. Using b-spline bases provides geometric flexibility as well as many computational advantages and permits particularly efficient and elegant implementations. This is described for a fairly general discretization which covers all principal features of b-spline elements.

The generalized minimum residual method (GMRES) is well known for solving large nonsymmetric systems of linear equations. It generally uses restarting, which slows the convergence. However, some information can be retained at the time of the restart and used in the next cycle. We present algorithms that use implicit restarting in order to retain this information. Approximate eigenvectors determ...

In this paper‎, ‎a modern method is presented to solve a class of fractional optimal control problems (FOCPs) indirectly‎. ‎First‎, ‎the necessary optimality conditions for the FOCP are obtained in the form of two fractional differential equations (FDEs)‎. ‎Then‎, ‎the unknown functions are approximated by the hybrid functions‎, ‎including Bernoulli polynomials and Block-pulse functions based o...

We derive error bounds for the Rayleigh-Ritz method for the approximation to extremal eigenpairs of a symmetric matrix. The bounds are expressed in terms of the eigenvalues of the matrix and the angle between the subspace and the eigenvector. We also present a sharp bound.

The convergence analysis of the bilinear finite element method to a class of non-linear degenerate wave equation on anisotropic meshes is considered in this paper. Moreover, the global superconvergence for semidiscrete scheme is proposed through interpolation instead of the Ritz Volterra projection of the exact solution.

The aim of this paper is to compare the static deflections and stress results of layered and functionally graded composite beams under static load. In the comparison study, the results obtained for a cantilever beam under point load. The Timoshenko beam and the Euler-Bernoulli beam theories are used in the beam model. The energy based Ritz method is used for the solution of the problem and alge...

In the recent years, many direct methods have been developed to construct travelling wave solutions to the nonlinear partial differential equations (NLPDEs), such as the trigonometric function series method [1, 2], the modified mapping method and the extended mapping method [3], the modified trigonometric function series method [4], the dynamical system approach and the bifurcation method [5], ...

We consider the stability and convergence analysis of pressure stabilized finite element approximations of the transient Stokes’ equation. The analysis is valid for a class of symmetric pressure stabilization operators, but also for standard, inf-sup stable, velocity/pressure spaces without stabilization. Provided the initial data is chosen as a specific (method dependent) Ritz-projection, we g...