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Numerical solution of the Lippmann-Schwinger equation by approximate approximations
Dipartimenta di Matematica, Universita La Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy, Department of Mathematics, University of Linköping, 581 83 Linköping, Sweden, Weierstrass Inst. Appl. Anal. S., Mohrenstr. 39, 10117 Berlin, Germany.
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
Dipartimenta di Matematica, Universita La Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy, Department of Mathematics, University of Linköping, 581 83 Linköping, Sweden, Weierstrass Inst. Appl. Anal. S., Mohrenstr. 39, 10117 Berlin, Germany.
2004 (English)In: Journal of Fourier Analysis and Applications, ISSN 1069-5869, E-ISSN 1531-5851, Vol. 10, no 6, 645-660 p.Article in journal (Refereed) Published
Abstract [en]

A new method for the numerical solution of volume integral equations is proposed and applied to a Lippmann-Schwinger type equation in diffraction theory. The approximate solution is represented as a linear combination of the scaled and shifted Gaussian. We prove spectral convergence of the method up to some negligible saturation error. The theoretical results are confirmed by a numerical experiment.

Place, publisher, year, edition, pages
2004. Vol. 10, no 6, 645-660 p.
Keyword [en]
Approximation with Gaussians, Collocation, Cubatures, Helmholtz equation, Lippmann-Schwinger equation
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-45593DOI: 10.1007/s00041-004-3080-zOAI: oai:DiVA.org:liu-45593DiVA: diva2:266489
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2017-12-13

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Maz´ya, Vladimir G.

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