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

Svyatoslav I. Solodushkin ^[1] ; Irina F. Yumanova ^[1] ; Rob H. De Staelen ^[2]
1. [1] Ural Federal University
  
  Ural Federal University
  
  Rusia
2. [2] Ghent University
  
  Ghent University
  
  Arrondissement Gent, Bélgica
Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 289, Nº 1 (1 December 2015), 2015, págs. 322-330
Idioma: inglés
DOI: 10.1016/j.cam.2014.12.032
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Resumen
- 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.