First order partial differential equations with time delay and retardation of a state variable

We construct a finite difference scheme for the numerical solution of a first order partial differential equation with a time delay and retardation of a state variable. Such equations are used to model the dynamics of structured cell populations when age and maturity level are taken into account. Fo...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2015-12, Vol.289, p.322-330
Main Authors: Solodushkin, Svyatoslav I., Yumanova, Irina F., De Staelen, Rob H.
Format: Article
Language:English
Subjects:
Approximation
Convergence
Difference scheme
Finite difference method
Mathematical analysis
Mathematical models
Partial delay differential equation
Partial differential equations
Retardation
State variable
Time delay
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Summary:We construct a finite difference scheme for the numerical solution of a first order partial differential equation with a time delay and retardation of a state variable. Such equations are used to model the dynamics of structured cell populations when age and maturity level are taken into account. For the supplied difference schemes the order of approximation, stability and convergence order are studied. We illustrate the obtained results with a test example.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2014.12.032