Dynamic von-Kármán plate models consist of three coupled non-linear, time-dependent partial differential equations. These equations have been recently solved numerically [Kirby, R., Yosibash, Z., 2004. Solution of von-Kármán dynamic non-linear plate equations using a pseudo-spectral method. Comp. Meth. Appl. Mech. Eng. 193 (6–8) 575–599 and Yosibash, Z., Kirby, R., Gottlieb, D., 2004. Pseudo-sp...

Abstract We consider solitary-wave solutions of the generalized Burger’s-Fisher equation ∂Ψ ∂t + αΨ δ ∂Ψ ∂x − ∂ 2Ψ ∂x2 = βΨ(1 − Ψδ). In this paper, we present a new method for solving of the generalized Burger’s-Fisher equation by using the collocation formula for calculating spectral differentiation matrix for Chebyshev-Gauss-Lobatto point. To reduce round-off error in spectral collocation met...

This paper analyzes the stability and convergence of the Fourier pseudospectral method coupled with a variety of specially designed time-stepping methods of up to fourth order, for the numerical solution of a three dimensional viscous Burgers’ equation. There are three main features to this work. The first is a lemma which provides for an L2 and H 1 bound on a nonlinear term of polynomial type,...

in this paper, the chebyshev spectral collocation method(cscm) for one-dimensional linear hyperbolic telegraph equation is presented. chebyshev spectral collocation method have become very useful in providing highly accurate solutions to partial differential equations. a straightforward implementation of these methods involves the use of spectral differentiation matrices. firstly, we transform ...

Efficient and safe battery charge control is an important prerequisite for large-scale deployment of clean energy systems. This paper proposes an innovative approach to devising optimally health-conscious fast-safe charge protocols. A multiobjective optimal control problem is mathematically formulated via a coupled electro-thermal-aging battery model, where electrical and aging sub-models depen...

in this paper, a numerical efficient method is proposed for the solution of time fractionalmobile/immobile equation. the fractional derivative of equation is described in the caputosense. the proposed method is based on a finite difference scheme in time and legendrespectral method in space. in this approach the time fractional derivative of mentioned equationis approximated by a scheme of order o...

— The conservation and convergence properties o f spectral Fourier methods for the numerical approximation o f the Korteweg-de Vries équation are analyzed. It is proven thaï the (aliased) collocation pseudospectral method enjoys the same convergence properties as the spectral Galerkin method, which is less effective from the computational point ofview. This resuit provides a précise mathematica...

the present paper investigates the potential application of graphene sheets with attached nanoparticles as resonant sensors by introducing a nonlocal shear deformation plate model. to take into account an elastic connection between the nanoplate and the attached nanoparticle, the nanoparticle is considered as a mass-spring system. then, a combination of pseudo-spectral and integral quadrature m...

In this paper, the Chebyshev spectral collocation method(CSCM) for one-dimensional linear hyperbolic telegraph equation is presented. Chebyshev spectral collocation method have become very useful in providing highly accurate solutions to partial differential equations. A straightforward implementation of these methods involves the use of spectral differentiation matrices. Firstly, we transform ...