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Volume 3, Issue 3
Finite Volume Scheme for Multiple Fragmentation Equations

RAJESH KUMAR∗ AND JITENDRA KUMAR

Int. J. Numer. Anal. Mod. B, 3 (2012), pp. 270-284

Published online: 2012-03

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  • Abstract
In this paper we study a finite volume approximation for the conservative formulation of multiple fragmentation models. We investigate the convergence of the numerical solutions towards a weak solution of the continuous problem by considering locally bounded kernels. The proof is based on the Dunford-Pettis theorem by using the weak L^1 compactness method. The analysis of the method allows us to prove the convergence of the discretized approximated solution towards a weak solution to the continuous problem in a weighted L^1 space.
  • Keywords

Finite volume Fragmentation Convergence Particle

  • AMS Subject Headings

65R20 45K05 35L65

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAMB-3-270, author = {RAJESH KUMAR∗ AND JITENDRA KUMAR}, title = {Finite Volume Scheme for Multiple Fragmentation Equations}, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2012}, volume = {3}, number = {3}, pages = {270--284}, abstract = {In this paper we study a finite volume approximation for the conservative formulation of multiple fragmentation models. We investigate the convergence of the numerical solutions towards a weak solution of the continuous problem by considering locally bounded kernels. The proof is based on the Dunford-Pettis theorem by using the weak L^1 compactness method. The analysis of the method allows us to prove the convergence of the discretized approximated solution towards a weak solution to the continuous problem in a weighted L^1 space.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/283.html} }
TY - JOUR T1 - Finite Volume Scheme for Multiple Fragmentation Equations AU - RAJESH KUMAR∗ AND JITENDRA KUMAR JO - International Journal of Numerical Analysis Modeling Series B VL - 3 SP - 270 EP - 284 PY - 2012 DA - 2012/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnamb/283.html KW - Finite volume KW - Fragmentation KW - Convergence KW - Particle AB - In this paper we study a finite volume approximation for the conservative formulation of multiple fragmentation models. We investigate the convergence of the numerical solutions towards a weak solution of the continuous problem by considering locally bounded kernels. The proof is based on the Dunford-Pettis theorem by using the weak L^1 compactness method. The analysis of the method allows us to prove the convergence of the discretized approximated solution towards a weak solution to the continuous problem in a weighted L^1 space.
RAJESH KUMAR∗ AND JITENDRA KUMAR. (2012). Finite Volume Scheme for Multiple Fragmentation Equations. International Journal of Numerical Analysis Modeling Series B. 3 (3). 270-284. doi:
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