Related Experiment Video

Updated: Oct 21, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

High-Order BUG Dynamical Low-Rank Integrators Based on Explicit Runge-Kutta Methods

Fabio Nobile1, Sébastien Riffaud1

  • 1CSQI Chair, École Polytechnique Fédérale de Lausanne, Lausanne, 1015 Switzerland.

Journal of Scientific Computing
|October 20, 2026
PubMed

Keywords:
Basis-Update & Galerkin integratorsDynamical low-rank approximationMatrix differential equationsRunge–Kutta methodsStructure-preserving method

Related Concept Videos

Approximate Integration01:24

Approximate Integration

In many practical and theoretical contexts, the exact value of a definite integral may be inaccessible. This limitation typically arises when the antiderivative of a function is either unknown or cannot be expressed in a closed mathematical form. Alternatively, it can occur when a function is defined not by a formula but by a finite set of empirical data points, such as those collected during experiments. In these cases, approximate integration techniques provide a valuable solution.One of the...
Linear Differential Equations01:27

Linear Differential Equations

The integrating factor method provides a systematic way to solve first-order linear differential equations, especially those that cannot be handled by separation of variables. This method is particularly useful in modeling time-dependent physical systems influenced by both constant inputs and resistive forces. A common example is the motion of a car subjected to a constant engine force while experiencing air resistance proportional to its velocity.In such scenarios, Newton’s second law yields a...
Improper Integrals: Infinite Intervals01:29

Improper Integrals: Infinite Intervals

An integral is classified as improper due to an infinite interval when at least one of its limits of integration extends to positive or negative infinity. In such cases, the region under the curve is unbounded, and standard techniques for evaluating definite integrals are not directly applicable. Instead, the improper integral is defined through a limiting process that allows one to determine whether the accumulated area remains finite despite the infinite domain.Application to Exponential...
Improper Integrals: Discontinuous Integrands01:28

Improper Integrals: Discontinuous Integrands

Evaluating Areas Under Curves with DiscontinuitiesA definite integral is considered improper when the integrand is discontinuous at one of the limits of integration. This occurs when the function is undefined or becomes infinite at an endpoint, making the corresponding region under the curve unbounded. Such behavior is commonly associated with vertical asymptotes at the boundary of the interval. To properly define and evaluate these integrals, a limiting process is used to determine whether a...
Double Integrals Over General Regions01:18

Double Integrals Over General Regions

Double integrals are often used to measure quantities distributed across two-dimensional regions, such as rainfall over a lake, heat across a metal plate, or population density over land. In many practical situations, the region of interest does not have straight boundaries and cannot be described conveniently as a rectangle. Instead, the region may have curved or irregular edges. To evaluate integrals over such domains, the region is embedded inside a larger rectangular region where...
Changing the Order of Integration in Double Integrals01:21

Changing the Order of Integration in Double Integrals

Double integrals provide a practical method for determining the volume of liquid contained in tanks with irregularly shaped sides. To estimate the total volume, the base region of the tank is divided into many very small rectangular sections. Each section forms the base of a thin column of liquid, and the volumes of all these columns are added together across the entire region. This process produces an accurate representation of the total liquid volume inside the tank.The limits of integration...