Titlebook: Integral Equation Methods for Evolutionary PDE; A Convolution Quadra Lehel Banjai,Francisco-Javier Sayas Book 2022 Springer Nature Switzerl

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Some Examples of Causal Convolutions,This chapter introduces the basic ideas of causal convolutions and convolution equations. The main tool is the Laplace transform, which we briefly introduce. The concepts are described by a collection of examples of increasing difficulty culminating in the single layer potential representation of the solution of an acoustic transmission problem.

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Boundary-Field Formulations,le. We describe the analysis of the fully discrete system in two cases: the simpler case where the same time-discretisation is used in the interior and exterior domain and the more complex one, where an implicit scheme is used in the exterior and explicit in the interior.

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Transient Electromagnetism,risingly similar to the acoustic case. All the estimates for the discretisation by linear-multistep or Runge-Kutta convolution quadrature follow directly from the theory described in previous chapters.