论文标题
用于与合并和排斥跳跃的空间种群动力学模型的数值解的算法
Algorithm for numerical solutions to the kinetic equation of a spatial population dynamics model with coalescence and repulsive jumps
论文作者
论文摘要
提出了一种算法，用于查找动力学方程的数值解，该方程描述了放置在$ \ mathbb {r}^d（d \ geq 1）$中的无限点系统系统。粒子以配对的排斥进行随机跳跃，在此过程中也可以合并。动力学方程是一种基本上是非线性和非局部间差方程，几乎无法通过分析求解。该算法的推导基于时空离散化，边界条件，复合辛普森和梯形规则，runge-kutta方法，可调节的系统大小方案等。然后将算法应用于具有各种初始条件的方程式的一维版本。结果表明，对于模型参数的特殊选择，解决方案可能具有不可思议的时间行为。还对获得的结果进行了数值误差分析。
An algorithm is proposed for finding numerical solutions of a kinetic equation that describes an infinite system of point articles 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 derivation of the algorithm is based on the use of space-time discretization, boundary conditions, composite Simpson and trapezoidal rules, Runge-Kutta methods, adjustable system-size schemes, etc. The algorithm is then applied to the one-dimensional version of the equation with various initial conditions. It is shown that for special choices of the model parameters, the solutions may have unexpectable time behaviour. A numerical error analysis of the obtained results is also carried out.
