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Numerical solution to a nonlinear McKendrick-Von Foerster equation with diffusion

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Abstract

An implicit finite difference scheme is presented to approximate the solution to the McKendrick-Von Foerster equation with diffusion (M-V-D). The notion of upper solution is introduced and used effectively with aid of discrete maximum principle to study the well-posedness and stability of the numerical scheme. A relation between the numerical solutions to the M-V-D and the steady state problem is established.

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Acknowledgements

The authors are grateful to the anonymous reviewers for their helpful suggestions and comments which improved the quality of the manuscript.

Funding

The first author received financial support from CSIR (Ref.: 09/414(1154)/2017-EMR-I) for his research. The second author is supported by Department of Science and Technology, India, under MATRICS (MTR/2019/000848).

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of Hyderabad, Hyderabad, 500046, India

    Joydev Halder & Suman Kumar Tumuluri

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  1. Joydev Halder
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  2. Suman Kumar Tumuluri
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Correspondence to Joydev Halder.

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Halder, J., Tumuluri, S.K. Numerical solution to a nonlinear McKendrick-Von Foerster equation with diffusion. Numer Algor 92, 1007–1039 (2023). https://doi.org/10.1007/s11075-022-01328-5

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