Abstract—A reasonably accurate solution of the balance equation for a substance is obtained for a predetermined number of nuclei of a new phase in the nucleation kinetics. This solution is necessary for the adequate description of secondary nucleation and accurate determination of the number of nuclei of a new phase. The approximation is constructed by studying the characteristic properties of the solution at various stages of evolution. In particular, iterations, quadratic approximation, asymptotic formula, relaxation solution, and deformed relaxation are constructed. As a result, a solution that is accurate for the time intervals up to the beginning of precondensation is obtained.

中文翻译：

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构造一阶相变动力学中新相核数已知的平衡方程的解的近似方法

摘要—对于成核动力学中预定数量的新相核，可以获得一种物质平衡方程的合理准确的解。该解决方案对于充分描述二次成核和准确确定新相的核数是必需的。通过研究演化的各个阶段的特征特性来构造近似值。特别地，构造迭代，二次逼近，渐近公式，松弛解和变形松弛。结果，获得了对于直到预冷凝开始为止的时间间隔都是准确的解决方案。