Geodesic
Effective solution of the problem of motion of an infinite string with an attached point mass
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 1, pp. 105-112
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The Cauchy problem for the equation of motion of a string with a point mass is considered. By applying the convolution method for Fourier expansions, the solution of the problem is expressed in the form of quadrature rules in terms of the solution of the classical Cauchy problem with no point mass with the same equation and initial functions. As an example, a finite-form solution of the problem is found and the corresponding plots of the string near the point mass are constructed with a constant time step. 
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S. E. Kholodovskii. Effective solution of the problem of motion of an infinite string with an attached point mass. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 1, pp. 105-112. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_1_a8/

[1] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Nauka, M., 1972

[2] Belotserkovskii O. M., “Neustanovivshiesya kolebaniya beskonechnoi struny, nesuschei sosredotochennuyu massu i podderzhivaemuyu uprugovyazkimi podveskami”, Prikl. matem. i mekhan., 75:5 (2011), 791–812

[3] Kulterbaev Kh. P., Islamova O. V., “Matematicheskaya model kolebanii podveshennoi struny s sosredotochennoi massoi”, Izv. vyssh. uchebn. zavedenii. tekhn. nauki, 2007, no. 4, 41–46

[4] Milovidov A. E., Sharov G. S., “Problema ustoichivosti dlya zamknutoi relyativistskoi struny s tochechnoi massoi”, Vestnik Tverskogo GU. Ser. Fizika, 9(15):2 (2005), 114–123

[5] Kats I. S., “Opisanie mnozhestva spektralnykh funktsii regulyarnoi struny, nesuschei sosredotochennuyu massu na kontse, svobodnom ot granichnykh uslovii”, Izvestiya vyssh. uchebn. zavedenii. Matematika, 1974, no. 7, 27–33

[6] Chechkin G. A., “Rasscheplenie kratnogo sobstvennogo znacheniya v zadache o kontsentrirovannykh massakh”, Uspekhi matem. nauk, 59:4 (2004), 205–206 | DOI

[7] Oleinik O. A., Soboleva T. S., “O sobstvennykh kolebaniyakh neodnorodnoi struny s konechnym chislom prisoedinennykh mass”, Uspekhi matem. nauk, 43:4 (1988), 187–188

[8] Golovatyi Yu. D., “O sobstvennykh kolebaniyakh i sobstvennykh chastotakh uprugogo strezhnya s prisoedinennoi massoi”, Uspekhi matem. nauk, 43:4 (1988), 173–174

[9] Melnik T. A., Popov A. V., “Asimptoticheskii analiz kraevykh i spektralnykh zadach v tonkikh perforirovannykh oblastyakh s bystro izmenyayuscheisya tolschinoi i razlichnymi predelnymi razmernostyami”, Matem. sb., 203:8 (2012), 97–124 | DOI

[10] Melnik T. A., Nazarov S. A., “Asimptoticheskii analiz zadachi Neimana na soedinenii tela s tonkimi tyazhelymi sterzhnyami”, Algebra i analiz, 12:2 (2000), 188–238

[11] Gomes D., Nazarov S. A., Peres M. E., “Formalnaya asimptotika sobstvennykh chastot kolebanii uprugogo trekhmernogo tela s kontsentrirovannymi massami”, Zap. nauchn. semin. POMI, 342, 2007, 31–76

[12] Peres M. E., Chechkin G. A., Yablokova E. I., “O sobstvennykh kolebaniyakh tela s “legkimi” kontsentrirovannymi massami na poverkhnosti”, Uspekhi matem. nauk, 57:6 (2002), 195–196 | DOI

[13] Kholodovskii S. E., “Metod svertyvaniya razlozhenii Fure v reshenii kraevykh zadach s peresekayuschimisya liniyami sopryazheniya”, Zh. vychisl. matem. i matem. fiz., 47:9 (2007), 1550–1556

[14] Kholodovskii S. E., “Metod svertyvaniya razlozhenii Fure. Sluchai obobschennykh uslovii sopryazheniya tipa treschiny (zavesy) v kusochno-neodnorodnykh sredakh”, Differents. ur-niya, 45:6 (2009), 855–859