Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

1.8K
Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
1.8K
Bernoulli's Equation: Problem Solving01:16

Bernoulli's Equation: Problem Solving

1.5K
A Venturi meter is essential for measuring fluid flow rates in pipelines. It utilizes the relationship between fluid velocity and pressure described by Bernoulli's equation. When installed in a sewage system, the Venturi meter accurately determines the wastewater flow rate by measuring pressure differences.
The first step is to compute the cross-sectional areas of the pipe and the Venturi throat to analyze the pressure difference indicated by the pressure gauge. Next, the continuity...
1.5K
Clausius-Clapeyron Equation02:35

Clausius-Clapeyron Equation

59.8K
The equilibrium between a liquid and its vapor depends on the temperature of the system; a rise in temperature causes a corresponding rise in the vapor pressure of its liquid. The Clausius-Clapeyron equation gives the quantitative relation between a substance’s vapor pressure (P) and its temperature (T); it predicts the rate at which vapor pressure increases per unit increase in temperature.
59.8K
Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

3.6K
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
3.6K
Navier–Stokes Equations01:28

Navier–Stokes Equations

909
For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
909
Conduction, Convection and Radiation: Problem Solving01:20

Conduction, Convection and Radiation: Problem Solving

1.5K
There are three methods by which heat transfer can take place: conduction, convection, and radiation. Each method has unique and interesting characteristics, but all three have two things in common: they transfer heat solely because of a temperature difference; and the greater the temperature difference, the faster the heat transfer.
In order to solve a problem related to heat transfer, first of all, the situation needs to be examined to determine the type of heat transfer involved. This could...
1.5K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Intravenous lipid emulsion improves recovery time and quality from isoflurane anaesthesia: a double-blind clinical trial.

Basic & clinical pharmacology & toxicology·2014
Same author

Improvement of matrix-assisted laser desorption/ionization time-of-flight mass spectrometry for identification of clinically important Candida species.

Clinical laboratory·2014
Same author

Genetic engineering of the green alga Chlorella zofingiensis: a modified norflurazon-resistant phytoene desaturase gene as a dominant selectable marker.

Applied microbiology and biotechnology·2014
Same author

Successful one-stage extraction of an intracardiac and intravenous leiomyoma through the right atrium under transesophageal ultrasound monitoring.

Canadian journal of anaesthesia = Journal canadien d'anesthesie·2014
Same author

A particle swarm optimization variant with an inner variable learning strategy.

TheScientificWorldJournal·2014
Same author

Integrative Analysis of Cancer Diagnosis Studies with Composite Penalization.

Scandinavian journal of statistics, theory and applications·2014
Same journal

Retraction Note: A probabilistic approach toward evaluation of Internet rumor on COVID.

Soft computing·2026
Same journal

Complex and dynamic population structures: Synthesis, open questions, and future directions.

Soft computing·2025
Same journal

Retraction Note: Optimal path planning and data simulation of emergency material distribution based on improved neural network algorithm.

Soft computing·2025
Same journal

Retraction Note: A MobileNet-based CNN model with a novel fine-tuning mechanism for COVID-19 infection detection.

Soft computing·2025
Same journal

Retraction Note: Empirical evidence of effects of stringency amid Covid-19 pandemic spread.

Soft computing·2025
Same journal

Retraction Note: SCLAVOEM: hyper parameter optimization approach to predictive modelling of COVID-19 infodemic tweets using smote and classifier vote ensemble: Taiwo Olaleye.

Soft computing·2025
See all related articles

Related Experiment Video

Updated: Oct 7, 2025

Experimental Methodology for Estimation of Local Heat Fluxes and Burning Rates in Steady Laminar Boundary Layer Diffusion Flames
10:29

Experimental Methodology for Estimation of Local Heat Fluxes and Burning Rates in Steady Laminar Boundary Layer Diffusion Flames

Published on: June 1, 2016

12.0K

Crank-Nicolson method for solving uncertain heat equation.

Jin Liu1, Yifei Hao2

  • 1College of System Engineering, National University of Defense Technology, Changsha, 410073 China.

Soft Computing
|January 10, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces the Crank-Nicolson method for solving uncertain heat equations, offering improved stability over the Euler scheme. The new method effectively computes expected and extreme values for these equations.

Keywords:
Crank–Nicolson methodHeat equationLiu processNumerical solution

More Related Videos

Ice Generation and the Heat and Mass Transfer Phenomena of Introducing Water to a Cold Bath of Brine
08:16

Ice Generation and the Heat and Mass Transfer Phenomena of Introducing Water to a Cold Bath of Brine

Published on: March 13, 2017

14.0K
Author Spotlight: Simulation and Analysis of the Temperature Rise of Ring Main Unit Equipment
04:35

Author Spotlight: Simulation and Analysis of the Temperature Rise of Ring Main Unit Equipment

Published on: July 5, 2024

2.1K

Related Experiment Videos

Last Updated: Oct 7, 2025

Experimental Methodology for Estimation of Local Heat Fluxes and Burning Rates in Steady Laminar Boundary Layer Diffusion Flames
10:29

Experimental Methodology for Estimation of Local Heat Fluxes and Burning Rates in Steady Laminar Boundary Layer Diffusion Flames

Published on: June 1, 2016

12.0K
Ice Generation and the Heat and Mass Transfer Phenomena of Introducing Water to a Cold Bath of Brine
08:16

Ice Generation and the Heat and Mass Transfer Phenomena of Introducing Water to a Cold Bath of Brine

Published on: March 13, 2017

14.0K
Author Spotlight: Simulation and Analysis of the Temperature Rise of Ring Main Unit Equipment
04:35

Author Spotlight: Simulation and Analysis of the Temperature Rise of Ring Main Unit Equipment

Published on: July 5, 2024

2.1K

Area of Science:

  • Numerical Analysis
  • Partial Differential Equations
  • Uncertainty Quantification

Background:

  • Analytical solutions for uncertain heat equations are difficult to obtain.
  • The forward difference Euler method provides numerical solutions but can be unstable.
  • Existing numerical methods face challenges in stability for uncertain heat equations.

Purpose of the Study:

  • To propose a stable numerical method for solving uncertain heat equations.
  • To enhance the computation of expected and extreme values for solutions.
  • To demonstrate the effectiveness and stability of the proposed method.

Main Methods:

  • Implementation of the Crank-Nicolson method, an unconditionally stable implicit scheme.
  • Comparison of the Crank-Nicolson method with the forward difference Euler scheme.
  • Application of the Crank-Nicolson method to calculate expected and extreme values of solutions.

Main Results:

  • The Crank-Nicolson method exhibits unconditional stability, overcoming Euler scheme limitations.
  • Numerical examples confirm the superior stability of the Crank-Nicolson scheme.
  • The method successfully computes key characteristics like expected and extreme values.

Conclusions:

  • The Crank-Nicolson method is a stable and effective approach for uncertain heat equations.
  • This method enhances the reliability of numerical solutions for uncertain heat phenomena.
  • The study validates the availability and applicability of the Crank-Nicolson method.