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Existence and uniqueness of solutions to weakly singular integral-algebraic and integro-differential equations

Mikhail Bulatov, Pedro Lima, Ewa Weinmüller (2014)

Open Mathematics

We consider systems of integral-algebraic and integro-differential equations with weakly singular kernels. Although these problem classes are not in the focus of the main stream literature, they are interesting, not only in their own right, but also because they may arise from the analysis of certain classes of differential-algebraic systems of partial differential equations. In the first part of the paper, we deal with two-dimensional integral-algebraic equations. Next, we analyze Volterra integral...

Integral Equations VIA Saddle Point Problem for 2D Electromagnetic Problems

Nathalie Bartoli, Francis Collino (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

A new system of integral equations for the exterior 2D time harmonic scattering problem is investigated. This system was first proposed by B. Després in [11]. Two new derivations of this system are given: one from elementary manipulations of classical equations, the other based on a minimization of a quadratic functional. Numerical issues are addressed to investigate the potential of the method.

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