We investigate three-dimensional problems in solid mechanics with stochastic loading or material properties. To solve these problems, we use a spectral expansion of the solution and random inputs based on Askey-type orthogonal polynomials in terms of independent, identically distributed (i.i.d) random variables. A Galerkin procedure using these types of expansions, the generalized Polynomial Ch...

In this paper, we propose an iterative Kalman filtering scheme that has faster convergence and introduces less residual noise, when compared with the iterative scheme of Gibson, et al. This is achieved via the use of long and overlapped frames as well as using a tapered window with a large side lobe attenuation for linear prediction analysis. We show that the Dolph-Chebychev window with a −200 ...

in this study, a new efficient semi-analytical method is introduced to give approximate solutions of strongly nonlinear oscillators. the proposed method is based on combination of two different methods, the multi-step homotopy analysis method and spectral method, called the multi-step spectral homotopy analysis method (msham). in this method, firstly, we propose a new spectral homotopy analysis...

A method for computing highly accurate numerical solutions of 1D convection–diffusion equations is proposed. In this method, the equation is first discretized with respect to the spatial variable, transforming the original problem into a set of ordinary differential equations, and then the resulting system is integrated in time by the fourth-order Runge–Kutta method. Spatial discretization is d...

This paper presents a review of the current state-of-the-art of numerical methods for stochastic computations. The focus is on efficient high-order methods suitable for practical applications, with a particular emphasis on those based on generalized polynomial chaos (gPC) methodology. The framework of gPC is reviewed, along with its Galerkin and collocation approaches for solving stochastic equ...