This study presents a valuable in-depth comparison of statistical methods for the analysis of ecological time series data, and shows that different analyses can generate different conclusions, ...

This review aims to provide a comprehensive evaluation of the dynamics of the double pendulum, with a particular emphasis on its chaotic behavior. It examines the complicated and unpredictable ...

Abstract: Analytically solving complex or large-scale differential equations is often difficult or even impossible, making numerical integration methods indispensable. However, as all numerical ...

This advanced course explores the theory, development, and application of exponential integrators in the numerical solution of stiff systems of ordinary differential equations (ODEs). The key topics ...

This paper is dedicated to the proposition that, in order to take full advantage for real-time computations of highly parallel computers as can be expected to be available in the near future, much of ...

Euler Method: The simplest numerical method for solving ODEs, which uses the derivative to project forward. [ y_{n+1} = y_n + h \cdot f(x_n, y_n) ] Heun's Method (Improved Euler Method): A two-step ...

ABSTRACT: An entirely new framework is established for developing various single- and multi-step formulations for the numerical integration of ordinary differential equations. Besides polynomials, ...

William Bryant Gragg November 2, 1936 – December 25, 2016 Resident of Monterey William (Bill) Bryant Gragg, 80, died Sunday, December 25, 2016 at his home in Monterey following a brief illness. He ...

China Nuclear Power Technology Research Institute Co., Ltd., Shen Zhen, China The thermal–hydraulic dynamics in containment are governed by a system of stiff ordinary differential equations (ODEs). A ...

This paper presents In-Context Operator Networks (ICON), a neural network approach that can learn new operators from prompted data during the inference stage without requiring any weight updates.