Special Session 162: Computer-Assisted Proofs in Dynamical Systems

Efficient implementation of affine arithmetic for rigorous integration of delay differential equations
Ryoga Iwanami
Waseda University
Japan
Co-Author(s):    
Abstract:
In this talk, we introduce an efficient implementation of affine arithmetic. To compute tight enclosures of trajectories of dynamical systems, it is essential to suppress the wrapping effect. Although affine arithmetic can effectively reduce the wrapping effect, it tends to require significantly longer computation time compared to other methods. To address this issue, we accelerated affine arithmetic by utilizing error-free transformation, SIMD vectorization, and mixed-precision arithmetic. We will demonstrate its effectiveness by applying the accelerated implementation to several dynamical systems.