Search results for "Nyström method"

showing 3 items of 3 documents

Asymptotic stability of solutions to Volterra-renewal integral equations with space maps

2012

Abstract In this paper we consider linear Volterra-renewal integral equations (VIEs) whose solutions depend on a space variable, via a map transformation. We investigate the asymptotic properties of the solutions, and study the asymptotic stability of a numerical method based on direct quadrature in time and interpolation in space. We show its properties through test examples.

Asymptotic analysisApplied MathematicsNumerical analysisMathematical analysisvolterra renewalSpace mapVolterra integral equationMethod of matched asymptotic expansionsIntegral equationVolterra integral equationAsymptotic behaviorsymbols.namesakeExponential stabilityRenewal equationAsymptotologysymbolsNyström methodNumerical methodsAnalysisMathematicsJournal of Mathematical Analysis and Applications
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CAD of complex passive devices composed of arbitrarily shaped waveguides using Nyström and BI-RME methods

2004

In this paper, a novel computer-aided design (CAD) tool of complex passive microwave devices in waveguide technology is proposed. Such a tool is based on a very efficient integral-equation analysis technique that provides a full-wave characterization of discontinuities between arbitrarily shaped waveguides defined by linear, circular, and/or elliptical arcs. For solving the modal analysis of such arbitrary waveguides, a modified version of the well-known boundary integral-resonant-mode expansion (BI-RME) method using the Nyström approach, instead of the traditional Galerkin version of the method of moments, is proposed, thus providing significant savings on computational costs and implement…

RadiationModal analysisMethod of momentsCADMethod of moments (statistics)Condensed Matter Physicscomputer.software_genreTopologyWaveguide (optics)Waveguide componentsDiscontinuity (linguistics)Waveguide discontinuitiesTeoría de la Señal y ComunicacionesElectronic engineeringNyström methodComputer Aided DesignElectromagnetismoElectrical and Electronic EngineeringGalerkin methodcomputerIntegral equationsMathematics
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An adaptive method for Volterra–Fredholm integral equations on the half line

2009

AbstractIn this paper we develop a direct quadrature method for solving Volterra–Fredholm integral equations on an unbounded spatial domain. These problems, when related to some important physical and biological phenomena, are characterized by kernels that present variable peaks along space. The method we propose is adaptive in the sense that the number of spatial nodes of the quadrature formula varies with the position of the peaks. The convergence of the method is studied and its performances are illustrated by means of a few significative examples. The parallel algorithm which implements the method and its performances are described.

Volterra–Fredholm integral equationsApplied MathematicsDirect methodNumerical analysisMathematical analysisMathematicsofComputing_NUMERICALANALYSISParallel algorithmParallelismFredholm integral equationDirect QuadratureConvergence; Direct Quadrature; Parallelism; Volterra-Fredholm integral equations; Half lineIntegral equationVolterra integral equationQuadrature (mathematics)Half lineComputational Mathematicssymbols.namesakesymbolsVolterra-Fredholm integral equationsNyström methodConvergenceMathematicsJournal of Computational and Applied Mathematics
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