Numerical Solution of a Nonlinear Integro-Differential Equation

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...

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Bibliographic Details
Main Authors: Buša, Ján, Hnatič, Michal, Honkonen, Juha, Lučivjanský, Tomáš
Format: Conference Proceeding
Language:English
Subjects:
Algorithms
Approximation
Density
Differential equations
Integrals
Mathematical analysis
Mathematical models
Operators (mathematics)
Regularization
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Summary: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.
ISSN:2100-014X
2101-6275
2100-014X
DOI:10.1051/epjconf/201610802017