Numerical Solution of a Nonlinear Integro-Differential Equation
1 Department of Mathematics and Theoretical Informatics, FEE&I, Technical University, Košice, Slovakia
2 Faculty of Sciences, P. J. Šafarik University, Košice, Slovakia
3 Institute of Experimental Physics SAS, Košice, Slovakia
4 Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Moscow Region, Russia
5 Department of Military Technology, National Defence University, Helsinki, Finland
6 Fakultät für Physik, Universität Duisburg-Essen, D-47048 Duisburg, Germany
Published online: 9 February 2016
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.
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