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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     author = {S. E. Kholodovskii},
     title = {Effective solution of the problem of motion of an infinite string with an attached point mass},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {105--112},
     publisher = {mathdoc},
     volume = {55},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_1_a8/}
}
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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/