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Theoretical and numerical study of a free boundary problem by boundary integral methods

Michel Crouzeix, Philippe Féat, Francisco-Javier Sayas (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper we study a free boundary problem appearing in electromagnetism and its numerical approximation by means of boundary integral methods. Once the problem is written in a equivalent integro-differential form, with the arc parametrization of the boundary as unknown, we analyse it in this new setting. Then we consider Galerkin and collocation methods with trigonometric polynomial and spline curves as approximate solutions.

Theoretical and numerical study of a free boundary problem by boundary integral methods

Michel Crouzeix, Philippe Féat, Francisco-Javier Sayas (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we study a free boundary problem appearing in electromagnetism and its numerical approximation by means of boundary integral methods. Once the problem is written in a equivalent integro-differential form, with the arc parametrization of the boundary as unknown, we analyse it in this new setting. Then we consider Galerkin and collocation methods with trigonometric polynomial and spline curves as approximate solutions.

Time-Fractional Derivatives in Relaxation Processes: A Tutorial Survey

Mainardi, Francesco, Gorenflo, Rudolf (2007)

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: 26A33, 33E12, 33C60, 44A10, 45K05, 74D05,The aim of this tutorial survey is to revisit the basic theory of relaxation processes governed by linear differential equations of fractional order. The fractional derivatives are intended both in the Rieamann-Liouville sense and in the Caputo sense. After giving a necessary outline of the classica theory of linear viscoelasticity, we contrast these two types of fractiona derivatives in their ability to take into...

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