Numerical Solution of a Nonlinear Integro-Differential Equation
J. Bu\v{s}a, M. Hnati\v{c}, J. Honkonen, T. Lu\v{c}ivjansk\'y
TL;DR
This paper presents a numerical algorithm combining finite difference and regularization techniques to solve a nonlinear integro-differential equation modeling a single-species annihilation reaction, with results demonstrating its effectiveness.
Contribution
It introduces a novel numerical method for solving nonlinear integro-differential equations with divergent integrals in two dimensions.
Findings
The algorithm successfully solves the equation for the reaction model.
Regularization effectively handles divergent integrals in 2D.
Numerical results validate the method's accuracy.
Abstract
An algorithm for the numerical solution of a nonlinear integro-differential equation arising in the single-species annihilation reaction modeling is discussed. Finite difference method together with the linear approximation of the unknown function is considered. For divergent integrals presented in the equation for dimension a regularization is used. Some numerical results are presented.
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