Geodesic
Finite difference method for the parabolic problem with delta function
Kragujevac Journal of Mathematics, Tome 33 (2010), p. 71

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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.
Classification : 65M12
Keywords: Delta function, Sobolev norm, Convergence. 
Dejan R. Bojović. Finite difference method for the parabolic problem with delta function. Kragujevac Journal of Mathematics, Tome 33 (2010), p. 71 . http://geodesic.mathdoc.fr/item/KJM_2010_33_a5/
@article{KJM_2010_33_a5,
     author = {Dejan R. Bojovi\'c},
     title = {Finite difference method for the parabolic problem with delta function},
     journal = {Kragujevac Journal of Mathematics},
     pages = {71 },
     year = {2010},
     volume = {33},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2010_33_a5/}
}
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