Geodesic
Finite difference method for the parabolic problem with delta function
Kragujevac Journal of Mathematics, Tome 33 (2010) no. 1.

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

We investigate the convergence of difference schemes for the one-dimensional heat equation with the coefficient of the time derivative containing a Dirac delta distribution. An abstract operator method is applied for analyzing this equation. The convergence rate estimate of the order $\mathcal{O}$$(h)$ in a special discrete $\widetilde{W}^{2,1}_2$ Sobolev norm, compatible with the smoothness of the solution, is obtained. 
@article{KJM_2010_33_1_a5,
     author = {Dejan R. Bojovi\'c},
     title = {Finite difference method for the parabolic problem with delta function},
     journal = {Kragujevac Journal of Mathematics},
     pages = {71 - 82},
     publisher = {mathdoc},
     volume = {33},
     number = {1},
     year = {2010},
     url = {http://geodesic.mathdoc.fr/item/KJM_2010_33_1_a5/}
}
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Dejan R. Bojović. Finite difference method for the parabolic problem with delta function. Kragujevac Journal of Mathematics, Tome 33 (2010) no. 1. http://geodesic.mathdoc.fr/item/KJM_2010_33_1_a5/