On Computation of Lyapunov Exponents by QR Methods with Error Control for Semi-Linear DAEs

Hoang Linh Vu; Duy Truong Nguyen; Quang Tuyen Phan

doi:10.52825/dae-p.v3i.2632

Authors

Vu Hoang Linh Vietnam National University, Hanoi
Dr. Nguyen Duy Truong Tran Quoc Tuan University
Mr. Phan Quang Tuyen College of Artillery Officer’s Training

DOI:

https://doi.org/10.52825/dae-p.v3i.2632

Keywords:

Semi-Linear Differential-Algebraic Equations, Linearization, Lyapunov Exponents, Smooth QR Factorization, Embedded Runge-Kutta Methods, Error Control

Abstract

In this paper, we propose and analyze numerical methods for computing Lyapunov exponents of semi-linear differential-algebraic equations (DAEs), leveraging smooth QR factorizations and Runge-Kutta (RK) methods with error control and automatic step size selection. We demonstrate how both discrete and continuous QR approaches efficiently approximate Lyapunov exponents by simultaneously solving semi-linear DAEs and their linearized counterparts. The paper details the underlying algorithms, error analysis, and numerical integration techniques, focusing on half-explicit RK (HERK) and explicit singly diagonal implicit RK (ESDIRK) methods. We also provide implementation details and present numerical experiments to illustrate the efficiency of these methods.

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On Computation of Lyapunov Exponents by QR Methods with Error Control for Semi-Linear DAEs

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