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Clean Numerical Simulation
Clean Numerical Simulation
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Excellent- More about Clean Numerical Simulation
Clean Numerical Simulation (CNS) is a novel approach to numerical simulation that provides a convergent chaotic trajectory with lower numerical noise than the true physical solution, enabling accurate statistics stability checking. It reveals an incompleteness of the modern science paradigm and highlights the importance of reproducibility in physical experiments. CNS also proposes conjectures and open problems, such as a modified fourth Clay millennium problem, and opens the door to exploring the clean numerical world of chaos and turbulence.
Format: Hardback
Length: 144 pages
Publication date: 26 September 2023
Publisher: Taylor & Francis Ltd
This book delves into the fundamental principles of Clean Numerical Simulation (CNS), a groundbreaking approach proposed by the author in 2009. Unlike conventional algorithms, CNS offers a remarkable capability to generate convergent chaotic trajectories with significantly lower numerical noise compared to the true physical solution. This allows for precise and accurate calculations, providing a unique opportunity to examine the stability of chaos. Consequently, CNS introduces a novel concept of ultra-chaos, characterized by both trajectory instability and statistical instability, representing a higher level of disorder.
Interestingly, it is impossible to replicate experimental results of ultra-chaos even in a statistical sense. However, the reproducibility of physical experiments forms the cornerstone of modern science. Thus, ultra-chaos reveals an incompleteness of the modern science paradigm. Moreover, it sheds light on the importance of statistics stability as a prerequisite for the use of conventional algorithms, including direct numerical simulation (DNS).
Within the realm of Clean Numerical Simulation, several conjectures and open problems are proposed, including a modified fourth Clay millennium problem. Indeed, CNS opens the door for us to enter the clean numerical world of chaos and turbulence, offering a promising avenue for further exploration and discovery in the field of computational mathematics.
Dimension: 234 x 156 (mm)
ISBN-13: 9781032288093
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