In various fields of natural science, the chaotic systems of differential equations are considered more than 50 years. The correct prediction of the behaviour of solutions of dynamical model equations is important in understanding of evolution process and reduce uncertainty. However, often used numerical methods are unable to do it on large time segments. In this article, the author considers the modern numerical method and algorithm for constructing solutions of chaotic systems on the example of tumor growth model. Also a modification of Benettin's algorithm presents for calculation of Lyapunov exponents.

中文翻译：

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构造混沌系统解的精确数值方法和算法

在自然科学的各个领域中，微分方程的混沌系统被认为已有50多年的历史了。动力学模型方程解的行为正确预测对于理解演化过程和减少不确定性很重要。但是，常用的数值方法无法在较长的时间段上做到这一点。在本文中，作者以肿瘤生长模型为例，考虑了构建混沌系统解的现代数值方法和算法。贝纳汀算法的一个修改也提出了李雅普诺夫指数的计算。