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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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