In this Letter, a (2 + 1)-dimensional soliton equation is studied by He’s variational approach. The solitary solutions are obtained using the Ritz method.

We introduce a new and eecient Chebyshev-Legendre Galerkin method for elliptic problems. The new method is based on a Legendre-Galerkin formulation, but only the Chebyshev-Gauss-Lobatto points are used in the computation. Hence, it enjoys advantages of both the Legendre-Galerkin and Chebyshev-Galerkin methods.

Rayleigh–Ritz eigenvalue estimates for Hermitian matrices obey Cauchy interlacing, which has helpful implications for theory, applications, and algorithms. In contrast, few results about the Ritz values of non-Hermitian matrices are known, beyond their containment within the numerical range. To show that such Ritz values enjoy considerable structure, we establish regions within the numerical ra...

In this paper, we study the deep Ritz method for solving linear elasticity equation from a numerical analysis perspective. A modified formulation using $H^{1/2}(\Gamma_D)$ norm is introduced and analyzed in order to deal with (essential) Dirichlet boundary condition. We show that resulting provides best approximation among set of neural network (DNN) functions respect ``energy'' norm. Furthermo...

This paper describes an experimental study on the use of Ritz vectors for damage detection of a grid-type bridge model. A new procedure to extract Ritz vectors from experimental modal analysis is proposed and demonstrated using the test structure. Using appropriate load patterns, Ritz vectors can be made more sensitive to damage than modal vectors. The results indicate that the use of load-depe...