Geodesic
Approximate solution of a boundary value problem with a discontinuous solution
Daghestan Electronic Mathematical Reports, Tome 15 (2021), pp. 22-29

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Using spline-functions for three-point rational interpolants an approximate solution of the boundary value problem: $y^\prime +p(x) y=f(x)$, $y(a)=A$, $y(b)=B$ is constructed. In this case, the functions $p(x)$ and $f(x)$ are assumed to be continuous on the segment $[a,b]$ and it is allowed, that there exists a solution $y (x)$ that can have a discontinuity of the first kind with a jump at a given point $\tau\in (a, b)$.
Keywords: rational spline-function, differential equation, approximate solution. 
@article{DEMR_2021_15_a1,
     author = {A.-R. K. Ramazanov and A.-K. K. Ramazanov},
     title = {Approximate solution of a boundary value problem with a discontinuous solution},
     journal = {Daghestan Electronic Mathematical Reports},
     pages = {22--29},
     publisher = {mathdoc},
     volume = {15},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DEMR_2021_15_a1/}
}
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A.-R. K. Ramazanov; A.-K. K. Ramazanov. Approximate solution of a boundary value problem with a discontinuous solution. Daghestan Electronic Mathematical Reports, Tome 15 (2021), pp. 22-29. http://geodesic.mathdoc.fr/item/DEMR_2021_15_a1/