Finite-difference and pseudo-spectral methodsfor the numerical simulations of in vitro human tumor cellpopulation kinetics
Pseudo-spectral approximations areconstructed for the model equations describing the populationkinetics of human tumor cells in vitro and their responses toradiotherapy or chemotherapy. These approximations are moreefficient than finite-difference approximations. The spectralaccuracy of the pseudo-s...
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| Format: | Article |
| Language: | English |
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AIMS Press
2009-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.561 |
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| author | Z. Jackiewicz B. Zubik-Kowal B. Basse |
| author_facet | Z. Jackiewicz B. Zubik-Kowal B. Basse |
| author_sort | Z. Jackiewicz |
| collection | DOAJ |
| description | Pseudo-spectral approximations areconstructed for the model equations describing the populationkinetics of human tumor cells in vitro and their responses toradiotherapy or chemotherapy. These approximations are moreefficient than finite-difference approximations. The spectralaccuracy of the pseudo-spectral method allows us to resolve themodel with a much smaller number of spatial grid-points thanrequired for the finite-difference method to achieve comparableaccuracy. This is demonstrated by numerical experiments which show agood agreement between predicted and experimental data. |
| format | Article |
| id | doaj-art-304aada987df4ca8904b95d7eb3779e0 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2009-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-304aada987df4ca8904b95d7eb3779e02025-01-24T01:59:54ZengAIMS PressMathematical Biosciences and Engineering1551-00182009-05-016356157210.3934/mbe.2009.6.561Finite-difference and pseudo-spectral methodsfor the numerical simulations of in vitro human tumor cellpopulation kineticsZ. Jackiewicz0B. Zubik-Kowal1B. Basse2Department of Mathematics and Statistics, Arizona State University, Tempe, Arizona 85287Department of Mathematics and Statistics, Arizona State University, Tempe, Arizona 85287Department of Mathematics and Statistics, Arizona State University, Tempe, Arizona 85287Pseudo-spectral approximations areconstructed for the model equations describing the populationkinetics of human tumor cells in vitro and their responses toradiotherapy or chemotherapy. These approximations are moreefficient than finite-difference approximations. The spectralaccuracy of the pseudo-spectral method allows us to resolve themodel with a much smaller number of spatial grid-points thanrequired for the finite-difference method to achieve comparableaccuracy. This is demonstrated by numerical experiments which show agood agreement between predicted and experimental data.https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.561mathematicalmodelcell cycle dynamicspseudo-spectral methodspopulation kinetics of human cancercells in vitrohuman tumor cellsfinite-difference methods. |
| spellingShingle | Z. Jackiewicz B. Zubik-Kowal B. Basse Finite-difference and pseudo-spectral methodsfor the numerical simulations of in vitro human tumor cellpopulation kinetics Mathematical Biosciences and Engineering mathematicalmodel cell cycle dynamics pseudo-spectral methods population kinetics of human cancercells in vitro human tumor cells finite-difference methods. |
| title | Finite-difference and pseudo-spectral methodsfor the numerical simulations of in vitro human tumor cellpopulation kinetics |
| title_full | Finite-difference and pseudo-spectral methodsfor the numerical simulations of in vitro human tumor cellpopulation kinetics |
| title_fullStr | Finite-difference and pseudo-spectral methodsfor the numerical simulations of in vitro human tumor cellpopulation kinetics |
| title_full_unstemmed | Finite-difference and pseudo-spectral methodsfor the numerical simulations of in vitro human tumor cellpopulation kinetics |
| title_short | Finite-difference and pseudo-spectral methodsfor the numerical simulations of in vitro human tumor cellpopulation kinetics |
| title_sort | finite difference and pseudo spectral methodsfor the numerical simulations of in vitro human tumor cellpopulation kinetics |
| topic | mathematicalmodel cell cycle dynamics pseudo-spectral methods population kinetics of human cancercells in vitro human tumor cells finite-difference methods. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.561 |
| work_keys_str_mv | AT zjackiewicz finitedifferenceandpseudospectralmethodsforthenumericalsimulationsofinvitrohumantumorcellpopulationkinetics AT bzubikkowal finitedifferenceandpseudospectralmethodsforthenumericalsimulationsofinvitrohumantumorcellpopulationkinetics AT bbasse finitedifferenceandpseudospectralmethodsforthenumericalsimulationsofinvitrohumantumorcellpopulationkinetics |