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Characteristic Line Based Schemes for Solving a Quasilinear Hierarchical Size-Structured Model

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Abstract

New schemes, based on the characteristics line method, for solving a hierarchical size-structured model with nonlinear growth, mortality and reproduction rate are developed. The idea of the schemes is not to follow the characteristics from the initial condition, but for each time-step to find the origins of the grid nodes at the previous time level. Numerical tests, including comparison with exact solutions for the new schemes, are elaborated. Numerical results that confirm the theoretical order of convergence of the new schemes are presented.

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References

  1. Ackleh, A.S., Deng, K.: Existence-uniqueness of solutions for a nonlinear nonautonomous size-strustured population model: an upper-lower solution approach. Can. Appl. Math. Q. 8, 1–15 (2000)

    MATH  MathSciNet  Google Scholar 

  2. Ackleh, A.S., Deng, K., Hu, S.: A quasilinear hierarchical size-structured model: well-posedness and approximation. Appl. Math. Optim. 51, 35–59 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  3. Douglas, J., Russell, T.F.: Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures. SIAM J. Numer. Appl. 19, 871–885 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  4. Angelo, O., López-Marcos, J.C.: Numerical integration of fully nonlinear size-structured population models. Appl. Numer. Math. 50, 291–327 (2004)

    Article  MathSciNet  Google Scholar 

  5. Harten, A.: High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49, 357–393 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  6. Kostova, T.: An explicit third-order numerical method for size-structured population equations. Numer. Methods Partial Differ. Equ. 19, 1–21 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  7. Kraev, E.A.: Existence and uniqueness for height structured hierarchical population models. Nat. Resour. Model. 14, 45–70 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  8. Ito, K., Kappel, F., Peichl, G.: A fully discretized approximation scheme for size-structured population models. SIAM J. Numer. Anal. 28, 923–954 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  9. Marinov, T.T., Sakai, K., Marinova, R.S.: A numerical scheme based on characteristic line method for conservative advection-equations. Comput. Fluid Dyn. J. 10, 137–142 (2001)

    Google Scholar 

  10. Shen, J., Shu, C.-W., Zhang, M.: High resolution schemes for a hierarchical size-structured model. SIAM J. Numer. Anal. 45, 352–370 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  11. Shen, J., Shu, C.-W., Zhang, M.: A high order WENO scheme for a hierarchical size-structured population model. J. Sci. Comput. 33, 279–291 (2007)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Natural Sciences, Southern University at New Orleans, New Orleans, LA, 70126, USA

    Tchavdar T. Marinov

  2. Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, 70504, USA

    Keng Deng

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  1. Tchavdar T. Marinov
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  2. Keng Deng
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Correspondence to Tchavdar T. Marinov.

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Marinov, T.T., Deng, K. Characteristic Line Based Schemes for Solving a Quasilinear Hierarchical Size-Structured Model. J Sci Comput 46, 452–469 (2011). https://doi.org/10.1007/s10915-010-9413-y

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  • DOI: https://doi.org/10.1007/s10915-010-9413-y

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