Acessibilidade / Reportar erro
Computational & Applied Mathematics, Volume: 26, Número: 2, Publicado: 2007
  • Generalizations of Aitken's process for accelerating the convergence of sequences

    Brezinski, Claude; Redivo Zaglia, Michela

    Resumo em Inglês:

    When a sequence or an iterative process is slowly converging, a convergence acceleration process has to be used. It consists in transforming the slowly converging sequence into a new one which, under some assumptions, converges faster to the same limit. In this paper, new scalar sequence transformations having a kernel (the set of sequences transformed into a constant sequence) generalizing the kernel of the Aitken's delta2 process are constructed. Then, these transformations are extended to vector sequences. They also lead to new fixed point methods which are studied.
  • Angular analysis of two classes of non-polyhedral convex cones: the point of view of optimization theory

    Iusem, Alfredo; Seeger, Alberto

    Resumo em Inglês:

    There are three related concepts that arise in connection with the angular analysis of a convex cone: antipodality, criticality, and Nash equilibria. These concepts are geometric in nature but they can also be approached from the perspective of optimization theory. A detailed angular analysis of polyhedral convex cones has been carried out in a recent work of ours. This note focus on two important classes of non-polyhedral convex cones: elliptic cones in an Euclidean vector space and spectral cones in a space of symmetric matrices.
  • A transmission problem for the Timoshenko system

    Raposo, C.A.; Bastos, W.D.; Santos, M.L.

    Resumo em Inglês:

    In this work we study a transmission problem for the model of beams developed by S.P. Timoshenko [10]. We consider the case of mixed material, that is, a part of the beam has friction and the other is purely elastic. We show that for this type of material, the dissipation produced by the frictional part is strong enough to produce exponential decay of the solution, no matter how small is its size. We use the method of energy to prove exponential decay for the solution.
  • Grid generation and adaptation by functionals

    Khattri, Sanjay Kumar

    Resumo em Inglês:

    Accuracy of a simulation is strongly depend on the grid quality. Here, quality means orthogonality at the boundaries and quasi-orthogonality within the critical regions, smoothness, bounded aspect ratios, solution adaptive behavior, etc. We review various functionals for generating high quality structured quadrilateral meshes in two dimensional domains. Analysis of Winslow and Modified Liao functionals are presented. Numerical examples are also presented to support our theoretical analysis. We will demonstrate the use of the Area functional for generating adaptive quadrilateral meshes.
  • Classification of homogeneous quadratic conservation laws with viscous terms

    Wenstrom, Jane Hurley; Plohr, Bradley J.

    Resumo em Inglês:

    In this paper, we study systems of two conservation laws with homogeneous quadratic flux functions. We use the viscous profile criterion for shock admissibility. This criterion leads to the occurrence of non-classical transitional shock waves, which are sensitively dependent on the form of the viscosity matrix. The goal of this paper is to lay a foundation for investigating how the structure of solutions of the Riemann problem is affected by the choice of viscosity matrix. Working in the framework of the fundamental wave manifold, we derive a necessary and sufficient condition on the model parameters for the presence of transitional shock waves. Using this condition, we are able to identify the regions in the wave manifold that correspond to transitional shock waves. Also, we determine the boundaries in the space of model parameters that separate models with differing numbers of transitional regions.
  • Two approximate methods of a Cauchy problem for the Helmholtz equation

    Xiong, Xiang-Tuan; Fu, Chu-Li

    Resumo em Inglês:

    In this paper, we consider a Cauchy problem for the Helmholtz equation at fixed frequency, especially we give the optimal error bound for the ill-posed problem. Within the framework of general regularization theory, we present some spectral regularization methods and a modified Tikhonov regularization method to stabilize the problem. Moreover, Hölder-type stability error estimates are proved for these regularization methods. According to the regularization theory, the error estimates are order optimal. Some numerical results are reported.
Sociedade Brasileira de Matemática Aplicada e Computacional Sociedade Brasileira de Matemática Aplicada e Computacional - SBMAC, Rua Maestro João Seppe, nº. 900 , 16º. andar - Sala 163, 13561-120 São Carlos - SP Brasil, Tel./Fax: 55 16 3412-9752 - São Carlos - SP - Brazil
E-mail: sbmac@sbmac.org.br