Rok 2015

• A PAIR OF PERFECTLY CONDUCTING DISKS IN AN EXTERNAL FIELD

  Publikacja

  • N. Rylko
  • N. Ryłko

  - Mathematical Modelling and Analysis - Rok 2015

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• Analysis of Interspike-Intervals for the General Class of Integrate-and-Fire Models with Periodic Drive

  Publikacja

  • J. Signerska-Rynkowska

  - Mathematical Modelling and Analysis - Rok 2015

  We study one-dimensional integrate-and-fire models of the general type x˙=F (t, x) and analyze properties of the firing map which iterations recover consecutive spike timings. We impose very week constraints for the regularity of the function F (t, x), e.g. often it suffices to assume that F is continuous. If additionally F is periodic in t, using mathematical study of the displacement sequence of an orientation preserving circle...

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• Solving Boundary Value Problems for Second Order Singularly Perturbed Delay Differential Equations by ε-Approximate Fixed-Point Method

  Publikacja

  • Z. Bartoszewski
  • A. Baranowska

  - Mathematical Modelling and Analysis - Rok 2015

  In this paper, the boundary value problem for second order singularly perturbed delay differential equation is reduced to a fixed-point problem v = Av with a properly chosen (generally nonlinear) operator A. The unknown fixed-point v is approximated by cubic spline vh defined by its values vi = vh(ti) at grid points ti, i = 0, 1, ... ,N. The necessary for construction the cubic spline and missing the first derivatives at the boundary...

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