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- W2020792133 abstract "The purpose of this paper is to apply the method of intermediate matching for connecting the four local asymptotic solutions of the Van der Pol equation, given by Dorodnicyn [1]. It turns out that for the approximation of the periodic solution a fifth local solution is needed. The present approach results in a reduction of the computational work. The amplitude of the periodic solution is determined up to a higher order accuracy in v than has been done so far. Der Zweck dieser Arbeit ist die Methode der Zwischenanpassung für asymptotische Entwicklungen einzuführen und diese Methode auf die Verbindung der vier örtlichen Lösungen der Van der Pol Gleichung, die von Dorodnicyn angegeben wurden, anzuwenden. Es zeigt sich, dass für die Annäherung der periodischen Lösung eine fünfte örtliche Lösung benötigt wird. Das hier gezeigte Verfahren bewirkt eine Verminderung des Rechenaufwandes. Die Amplitude der periodischen Lösung wird mit einem höheren Genauigkeitsgrad in ν bestimmt als bisher. Цeлью дaннoй яaбoты являe;тcя пяилoЗeниe мeтoдa пяoмeЗУтoжнoй пoдгoнкя к acимптoтижecким яaЗлoЗeниям и Упoтяeблeниe этoгo мeтoдa пяи cшибaнии жeтыяeч лoкaльныч яeшeний Уяaбнeния бaн дeя Пoля, дaнныч Дoяoдницыным (3). oкaЗыбaeтcя, жтo для aппяoкcимияoбaния пeяиoдижecкoгo яeшeния нeoбчoдимo пocтяoeняe пятoгo лoкaльнoгo яeшeния. ПяeдлoЗeнный пoдчoд к Зaдaжe пяибoдит к Умeньшeнию oбъeмa быжиcлeний. aмплитУдa пeяиoдижecкoгo яeшeния oпяeдeлeнa c быcшeй cтeпeнью тoжнocти пo ν, жeм этo дeлaлocь дo cич пoя." @default.
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- W2020792133 date "1974-12-01" @default.
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- W2020792133 title "The method of matched asymptotic expansions for the periodic solution of the van der pol equation" @default.
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- W2020792133 doi "https://doi.org/10.1016/0020-7462(74)90008-0" @default.
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