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The Global Behavior of Finite Difference-Spatial Spectral Collocation Methods for a Partial Integro-differential Equation with a Weakly Singular Kernel
Jie Tang, Da Xu
Journal:

Numerical Mathematics: Theory, Methods and Applications / Volume 6 / Issue 3 / August 2013

Published online by Cambridge University Press:

28 May 2015, pp. 556-570

Print publication:

August 2013
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The z-transform is introduced to analyze a full discretization method for a partial integro-differential equation (PIDE) with a weakly singular kernel. In this method, spectral collocation is used for the spatial discretization, and, for the time stepping, the finite difference method combined with the convolution quadrature rule is considered. The global stability and convergence properties of complete discretization are derived and numerical experiments are reported.

Analysis of Convolution Quadrature Applied to the Time-Domain Electric Field Integral Equation
Q. Chen, P. Monk, X. Wang, D. Weile
Journal:

Communications in Computational Physics / Volume 11 / Issue 2 / February 2012

Published online by Cambridge University Press:

20 August 2015, pp. 383-399

Print publication:

February 2012
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We show how to apply convolution quadrature (CQ) to approximate the time domain electric field integral equation (EFIE) for electromagnetic scattering. By a suitable choice of CQ, we prove that the method is unconditionally stable and has the optimal order of convergence. Surprisingly, the resulting semi discrete EFIE is dispersive and dissipative, and we analyze this phenomena. Finally, we present numerical results supporting and extending our convergence analysis.

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2 results

The Global Behavior of Finite Difference-Spatial Spectral Collocation Methods for a Partial Integro-differential Equation with a Weakly Singular Kernel

Analysis of Convolution Quadrature Applied to the Time-Domain Electric Field Integral Equation