EPJ Web of Conferences (Jan 2016)

Numerical Solution of a Nonlinear Integro-Differential Equation

  • Buša Ján,
  • Hnatič Michal,
  • Honkonen Juha,
  • Lučivjanský Tomáš

DOI
https://doi.org/10.1051/epjconf/201610802017
Journal volume & issue
Vol. 108
p. 02017

Abstract

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A discretization algorithm for the numerical solution of a nonlinear integrodifferential equation modeling the temporal variation of the mean number density a(t) in the single-species annihilation reaction A + A → 0 is discussed. The proposed solution for the two-dimensional case (where the integral entering the equation is divergent) uses regularization and then finite differences for the approximation of the differential operator together with a piecewise linear approximation of a(t) under the integral. The presented numerical results point to basic features of the behavior of the number density function a(t) and suggest further improvement of the proposed algorithm.