Geodesic
Numerical solution of the linear inverse problem for the Euler–Darboux equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 5, pp. 848-857

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An inverse problem of the reconstruction of the right-hand side of the Euler–Darboux equation is studied. This problem is equivalent to the Volterra integral equation of the third kind with the operator of multiplication by a smooth nonincreasing function. Numerical solution of this problem is constructed using an integral representation of the solution of the inverse problem, the regularization method, and the method of quadratures. The convergence and stability of the numerical method is proved. 
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     author = {A. V. Glushak and T. T. Karakeev},
     title = {Numerical solution of the linear inverse problem for the {Euler{\textendash}Darboux} equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     publisher = {mathdoc},
     volume = {46},
     number = {5},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_5_a6/}
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A. V. Glushak; T. T. Karakeev. Numerical solution of the linear inverse problem for the Euler–Darboux equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 5, pp. 848-857. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_5_a6/