1. GENERAL FORM OF FINITE VOLUME METHODS We consider vertex-centered finite volume methods for solving diffusion type elliptic equation (1) −∇ · (K∇u) = f in Ω, with suitable Dirichlet or Neumann boundary conditions. Here Ω ⊂ R is a polyhedral domain (d ≥ 2), the diffusion coefficient K(x) is a d× d symmetric matrix function that is uniformly positive definite on Ω with components in L∞(Ω), and...

Computational modelling has received significant attention in the research community over the past few decades due to its pronounced contribution in better understanding of the nature, as well as in the development of advanced technologies. The modelling of more and more complex transport physical systems helps the community to address important issues, like identification of environmental prob...

1. Lax equivalence theorem 1 2. Abstract error analysis 2 3. Application: Finite difference method 3 4. Application: Finite element method 4 5. Application: Conforming Discretization of Variational Problems 5 6. Application: Perturbed Discretization 6 7. Application: Nonconforming finite element methods 7 8. Application: Finite volume method 7 9. Application: Superconvergence of linear finite e...

In this paper, we extend the sliding mode idea to a class of unmatched uncertain variable structure systems. This method is achieved with introducing a new terminal sliding variable and the finite time stability of proposed method is proved using a new particular finite time condition in both reaching and sliding phases. In reaching phase new sliding mode controller is derived to guarantee the ...

the harmony search algorithm is applied to optimum designs of a functionally graded (fg)-carbon naotubes (cnts)-reinforced pipes conveying fluid subjected to moving load. the structure is modeled by reddy cylindrical shell theory and the motion equations are derived by hamilton's principal. based on differential quadrature method (dqm), the dynamic displacement of system is derived. the le...