Special quadrature rules for Laplace transform inversion
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 12, pp. 2133-2139 Cet article a éte moissonné depuis la source Math-Net.Ru

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Quadrature rules for Laplace transform inversion are studied that are adapted to the inversion of transforms corresponding to slowly varying long processes characteristic of linear viscoelasticity problems. The convergence of special quadrature rules for Laplace transform inversion is proved.
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A. V. Lebedeva; V. M. Ryabov. Special quadrature rules for Laplace transform inversion. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 12, pp. 2133-2139. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_12_a1/

[1] Ditkin V. A., Prudnikov A. P., Integralnye preobrazovaniya i operatsionnoe ischislenie, Fizmatgiz, M., 1961

[2] Krylov V. I., Skoblya N. S., Metody priblizhennogo preobrazovaniya Fure i obrascheniya preobrazovaniya Laplasa, Nauka, M., 1974

[3] Poroshina N. I., Ryabov V. M., “O metodakh obrascheniya preobrazovaniya Laplasa”, Vestn. S.-Peterburgskogo un-ta. Ser. 1, 2011, no. 3, 55–64 | MR | Zbl

[4] Widder D. V., The Laplace transform, Princeton, 1946 | Zbl

[5] Dech G., Rukovodstvo k prakticheskomu primeneniyu preobrazovaniya Laplasa i $Z$-preobrazovaniya, Nauka, M., 1971 ; Doetsch G., Anleitund zum praktischen Gebrauch der Laplace-Transformation und der $Z$-Transformation, Munchen–Wien, 1967 | MR | MR | Zbl

[6] Lavrentev M. A., Shabat B. V., Metody teorii funktsii kompleksnogo peremennogo, Lan, M., 2002

[7] Lure A. I., Operatsionnoe ischislenie i ego prilozhenie k zadacham mekhaniki, GITTL, M.–L., 1951

[8] Slepyan L. I., Yakovlev Yu. S., Integralnye preobrazovaniya v nestatsionarnykh zadachakh mekhaniki, Sudostroenie, L., 1980 | MR | Zbl

[9] Rabotnov Yu. N., Elementy nasledstvennoi mekhaniki tverdykh tel, Nauka, M., 1977 | MR

[10] Ekelchik V. S., Ryabov V. M., “Ob ispolzovanii odnogo klassa nasledstvennykh yader v lineinykh uravneniyakh vyazkouprugosti”, Mekhan. kompozitnykh materialov, 1981, no. 3, 393–404

[11] Dzhrbashyan M. M., Integralnye preobrazovaniya i predstavleniya funktsii v kompleksnoi oblasti, Nauka, M., 1966

[12] Ryabov V. M., “O mnogochlenakh, voznikayuschikh pri chislennom obraschenii preobrazovaniya Laplasa”, Metody vychislenii, 12, Izd-vo Leningr. un-ta, L., 1981, 46–53 | MR

[13] Ryabov V. M., “Svoistva kvadraturnykh formul naivysshei stepeni tochnosti, primenyaemykh dlya obrascheniya preobrazovaniya Laplasa”, Zh. vychisl. matem. i matem. fiz., 29:7 (1989), 1083–1087 | MR

[14] Matveeva T. A., Ryabov V. M., “Obobschennye kvadraturnye formuly chislennogo obrascheniya preobrazovaniya Laplasa”, Vestn. S.-Peterburgskogo un-ta. Ser. 1, 2000, no. 4, 7–11 | MR | Zbl

[15] Bochner S., “Über Sturm–Liouvillesche Polynomsysteme”, Math. Zeischr., 29 (1929), 730–736 | DOI | MR | Zbl

[16] Smirnov V. I., Lebedev N. A., Konstruktivnaya teoriya funktsii kompleksnogo peremennogo, Nauka, M.–L., 1964 | MR