An algorithm is proposed for finding numerical solutions of a kinetic equation that describes an infinite system of point particles placed in \(\mathbb {R}^{d} (d \geq 1)\). 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.

提出了一种寻找动力学方程数值解的算法，该算法描述了置于\（\ mathbb {R} ^ {d}（d \ geq 1）\）中的点粒子的无限系统。粒子以成对排斥的方式执行随机跳跃，在此过程中它们也可以合并。动力学方程是一个本质上是非线性且非局部的积分微分方程，很难通过解析来求解。我们用来解决它的数值算法是基于时空离散，边界条件，辛普森和梯形规则，Runge-Kutta方法和可调系统大小方案。我们表明，对于模型参数的特殊选择，解决方案表现出异常的时间行为。还对获得的结果进行了数值误差分析。