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In a recent paper, the weighted essentially non-oscillatory (WENO) numerical scheme was applied to solve a multi-class Lighthill–Whitham–Richards (MCLWR) traffic flow model (J. Comput. Phys. 2003; 191:639–659). We discuss and present an enhanced WENO scheme with Lax–Friedrichs flux splitting by improving the estimation of the minimal characteristic speed of the MCLWR model, which is based on a set of inequalities of eigenvalues. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a new method for computing eigenvector derivatives with distinct and repeated eigenvalues for the real symmetric eigensystems is presented. Its main idea is to extend the governing equations of particular solutions for eigenvector derivatives. The extension is completed by requiring the solution to be mass orthogonal with respect to the distinct or repeated modes and adjusting the corresponding coefficients so that the coefficient matrix of the extended system is non-singular and has smaller condition number. Numerical examples are included to demonstrate the validity of the proposed method. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the eigenanalysis for the multiply-connected domain problem is studied by using the dual boundary element method. The occurrence and treatment of the spurious eigenvalues for multiply-connected domain problem are reviewed when the complex-valued BEM in used. Three approaches, Burton and Miller method, CHIEF concept and SVD updating techniques, are adopted to suppress the occurrence of spurious eigensolutions. Instead of using the singular and hypersingular formulations, the singularity-free methods, the null-field equation approach and the fictitious BEM, are also utilized to deal with the eigenproblem. Both the eigenvalues and eigenmodes are compared with the analytical solutions and those of FEM for the illustrative examples. Good agreement is made. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents an examination of the methods for the iterative modal perturbation and the application of these methods to the reanalysis of the eigenvalue problem. The iteration is based on the first-order modal perturbation. In two examples, it is shown that the iterative analysis has the advantage of accuracy over the addition of higher-order perturbations and it is an appropriate approach for the reanalysis of the eigenvalue problem in terms of accuracy and computational efficiency. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The lateral buckling of a simply supported symmetric thin-walled member is investigated. An energy equation for the lateral buckling of thin-walled member has been presented in which the effects of torsion and assumed warping are taken into account. Using variation method helps to derive the governing differential equation together with appropriated boundary conditions. The lateral buckling loads are obtained by solving the differential equation numerically using Galerkin's method of weighted residuals. The method presented in this paper yields the formula for computing the lateral buckling load that is very simple and straightforward. By the study, a very complex practical eigenvalue problem can be transformed into a very simple one. The results predicted with the analytical method are in good agreement with the ones obtained by experimental, finite integral, non-linear finite element methods and optimal analysis. The fast convergence of the method makes it possible to write the resulting formulae in a likely closed form which is very simple and very convenient to use. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we derive precise eigenvalue upper bounds for the discretized Stokes operator corresponding to two widely used schemes, namely the Q1–P0 mixed finite element and the marker and cell (MAC) finite difference scheme. We also highlight a remarkable property concerning the multiplicity of the eigenvalue μ=1 in the MAC case. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The natural vibration frequency of a bending beam with the adhesive mass is investigated in this paper. From the numerical solution of the governing equation under the relevant boundary conditions, we can define a function which is called the target function. It is proved that the problem for evaluating the natural vibration frequencies is equivalent to finding the zeros of the target function. The zeros of target function can be easily evaluated by the well-known half-division technique. It is also proved that the target function method provides one more effective way in this field. The presented numerical examples generally show that the adhesive mass has a significant influence on lowering the vibration frequency of bending beam. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Based on the same concept as generalized differential quadrature (GDQ), the method of Fourier expansion-based differential quadrature (FDQ) was developed and then applied to solve the Helmholtz eigenvalue problems with periodic and non-periodic boundary conditions. In FDQ, the solution of a partial differential equation is approximated by a Fourier series expansion. The details of the FDQ method and its implementation to sample problems are shown in this paper. It was found that the FDQ results are very accurate for the Helmholtz eigenvalue problems even though very few grid points are used. ©1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The serendipity (eight nodes) and Lagrange (nine nodes) plate elements following the Reissner–Mindlin irreducible formulation for the bending of plates are among the most popular in the finite element method. However, reduced integration on the shearing part of the stiffness matrix has to be performed in order to avoid locking of the mesh in the limit of thin plates, where numerical constraints are taking some degrees of freedom in order to be satisfied. This paper explains the competition between those constraints and the degrees of freedom, giving a mean to predict whether a mesh will lock or not. It also shows why the Lagrange element performs better than the serendipity element. Numerical results confirm this analysis. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The multiple reciprocity method is based on using higher-order fundamental solutions to eliminate domain integrals encountered in transient boundary integral formulations. The paper considers the numerical stability of this approach through an eigenvalue decomposition of the system matrix. We demonstrate that the multiple reciprocity method for transient heat conduction is stable only for appropriately chosen time steps. [ABSTRACT FROM AUTHOR]