An Accurate Numerical Method and Algorithm for Constructing Solutions of Chaotic Systems

TL;DR

This paper introduces a new numerical method and algorithm for accurately constructing solutions of chaotic systems, demonstrated on a tumor growth model, and includes a modified algorithm for calculating Lyapunov exponents.

Contribution

The paper presents a novel numerical approach and an improved algorithm for solving chaotic differential equations, enhancing long-term solution accuracy and Lyapunov exponent computation.

Findings

Improved accuracy in long-term solution prediction for chaotic systems

Effective algorithm for calculating Lyapunov exponents

Application demonstrated on tumor growth model

Abstract

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.