Conference
International Conference on Numerical Analysis and Its Applications
About: International Conference on Numerical Analysis and Its Applications is an academic conference. The conference publishes majorly in the area(s): Numerical analysis & Boundary value problem. Over the lifetime, 462 publication(s) have been published by the conference receiving 1474 citation(s).
Topics: Numerical analysis, Boundary value problem, Finite element method, Nonlinear system, Matrix (mathematics)
Papers
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TL;DR: It is shown that the well-known fully-discretized numerical models elaborated to the numerical solution of the abstract Cauchy problem can be interpreted in this manner.
Abstract: In this paper we consider the interaction of the operator splitting method and applied numerical method to the solution of the different sub-processes. We show that the well-known fully-discretized numerical models (like Crank-Nicolson method, Yanenko method, sequential alternating Marchuk method, parallel alternating method, etc.), elaborated to the numerical solution of the abstract Cauchy problem can be interpreted in this manner. Moreover, on the base of this unified approach a sequence of the new methods can be defined and investigated.
33 citations
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TL;DR: The theorems which state front motion description and stationary contrast structures formation are proved for parabolic, parabolic-periodic and integro-parabolic problems are proved.
Abstract: In the present paper we discuss father development of the general scheme of the asymptotic method of differential inequalities and illustrate it applying for some new important cases of initial boundary value problem for the nonlinear singularly perturbed parabolic equations,which are called in applications as reaction-diffusion-advection equations. The theorems which state front motion description and stationary contrast structures formation are proved for parabolic, parabolic-periodic and integro-parabolic problems.
33 citations
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24 Jun 1996
TL;DR: A class of higher order methods is investigated which can be viewed as implicit Taylor series methods based on Hermite quadratures, and a new rational predictor is used which can allow for larger step sizes on stiff problems.
Abstract: A class of higher order methods is investigated which can be viewed as implicit Taylor series methods based on Hermite quadratures. Improved automatic differentiation techniques for the claculation of the Taylor-coefficients and their Jacobians are used. A new rational predictor is used which can allow for larger step sizes on stiff problems.
31 citations
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TL;DR: An overview of the numerical methods for the solution of the Landau-Lifshitz-Gilbert equation is given and the coupling with Maxwell's equations is discussed.
Abstract: In this paper we give an overview of the numerical methods for the solution of the Landau-Lifshitz-Gilbert equation. We discuss advantages of the presented methods and perform numerical experiments to demonstrate their performance. We also discuss the coupling with Maxwell's equations.
28 citations
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TL;DR: A notion of mosaic ranks of a matrix is proposed which reduces a description of block matrices with low-rank blocks to a single number and an algorithm for computing upper estimates of the mosaic ranks is given.
Abstract: The fact that nonsingular coefficient matrices can be covered by blocks close to low-rank matrices is well known probably for years. It was used in some cost-effective matrix-vector multiplication algorithms. However, it has been never paid a proper attention in the matrix theory. To fill in this gap we propose a notion of mosaic ranks of a matrix which reduces a description of block matrices with low-rank blocks to a single number. A general algebraic framework is presented that allows one to obtain some theoretical estimates on the mosaic ranks. An algorithm for computing upper estimates of the mosaic ranks is given with some illustrations of its efficiency on model problems.
24 citations