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The particles perform random jumps with pair-wise repulsion in the course of which they can also merge. The kinetic equation is an essentially nonlinear and nonlocal integro-differential equation, which can hardly be solved analytically. The numerical algorithm which we use to solve it is based on a space-time discretization, boundary conditions, composite Simpson and trapezoidal rules, Runge-Kutta methods, and adjustable system-size schemes. We show that, for special choices of the model parameters, the solutions manifest unusual time behavior. A numerical error analysis of the obtained results is also carried out.<\/jats:p>","DOI":"10.1007\/s11075-020-00992-9","type":"journal-article","created":{"date-parts":[[2020,8,20]],"date-time":"2020-08-20T01:02:35Z","timestamp":1597885355000},"page":"895-919","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Algorithm for numerical solutions to the kinetic equation of a spatial population dynamics model with coalescence and repulsive jumps"],"prefix":"10.1007","volume":"87","author":[{"given":"Igor","family":"Omelyan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuri","family":"Kozitsky","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2596-3260","authenticated-orcid":false,"given":"Krzysztof","family":"Pilorz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,8,20]]},"reference":[{"key":"992_CR1","unstructured":"Arratia, R. 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