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Numerical Methods for PDEs, Spectral Behaviour and Asymptotic Properties of Structured Matrix Sequences
Submission Deadline: Mar. 30, 2017
Lead Guest Editor
Eric Ngondiep
Hydrological Research Centre, Institute for Geological and Mining Research, Yaoundé, Centre, Cameroon
Guest Editor
  • Professor Prof. Dr. Hamed Daei Kasmaei
    Department of Applied Mathematics and Computer Science, Islamic Azad University,Central Tehran Branch, Tehran, Iran, Tehran, Iran
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Introduction
The solution of large structured linear systems remains the limiting bottle-neck in much of Scientific Computing. Such standard linear systems come from applications in various fields of computational mathematics and fluid dynamics and are often modeled by integral and/or (partial) differential equations. We consider some real-world problems and trust issues such as network problems, hybrid methods for partial differential equations, formal methods for ordinary differential equations, socio-technical aspect of discretization of partial differential equations appearing in several contexts in numerical analysis, computational fluid dynamics, and applications. For a given problem we select and describe a numerical scheme and we analyze both stability and rate of convergence. When possible, we consider fast algorithms for solving by preconditioning technique the related systems with special attention to the minimization of the computational work. For nonlinear problems, numerical schemes and iterative methods exist, but crucial issues are the stability condition, error estimates and convergence speed of these iterative solvers. The use of special techniques (preconditioning, multilevel techniques) for accelerating the convergence and a careful study of the spectral properties of related matrices.

Aims and scope

1. Stability analysis of numerical schemes
2. Error estimates and convergence rate of numerical methods
3. Spectral behavior of preconditioned structures matrix sequences (circulants, Toeplitz, Hankel, g-circulants, g-Toeplitz...)
4. Spectral features of structured matrices (circulants, Toeplitz, Hankel, g-circulants, g-Toeplitz...)
5. Asymptotic properties of structured matrix sequences (circulants, Toeplitz, Hankel, g-circulants, g-Toeplitz...)
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