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Eminov Stefan Teoriya integro-differentsial.nykh uravneniy vibratornykh antenn


V rabote postroena strogaya teoriya integro-differentsial'nykh uravneniy vibratornykh antenn. V osnove teorii lezhit vydelenie glavnogo operatora i dokazatel'stvo togo, chto glavnyy operator yavlyaetsya simmetrichnym i polozhitel'no opredelennym v prostranstve kvadratichno summiruemykh funktsiy. Dokazano, chto integro-differentsial'noe uravnenie ekvivalentno uravneniyu Fredgol'ma vtorogo roda v energeticheskom prostranstve glavnogo operatora. Dlya resheniya integro-differentsial'nogo uravneniya predlozhen metod Galerkina na osnove polinomov Chebysheva vtorogo roda, umnozhennykh na vesovuyu funktsiyu. Analiz chislennykh raschetov pokazyvaet, chto v zadachakh difraktsii skhodimost' metoda Galerkina bystraya, a v zadachakh vozbuzhdeniya medlennaya. I prichina medlennoy skhodimosti svyazana s tem, chto v zadachakh vozbuzhdeniya pravaya chast' integro-differentsial'nogo uravneniya razlagaetsya v medlenno skhodyashchiysya ryad. Dlya preodoleniya ukazannoy trudnosti predlozhen novyy chislenno-analiticheskiy metod resheniya, kotoryy mozhno rassmotret' kak modifikatsiyu metoda Galerkina.

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