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

Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

4.3K
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.
4.3K
Linear Differential Equations01:27

Linear Differential Equations

284
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...
284
Major Losses in Pipes01:28

Major Losses in Pipes

2.1K
When a fluid flows through a pipe, it experiences energy losses due to frictional resistance along the pipe walls, known as major losses. These energy losses result in a pressure drop, which varies based on the flow conditions — whether laminar or turbulent — and the specific physical properties of the fluid and pipe.
Fluid flow can be classified as laminar or turbulent, primarily based on the Reynolds number. This dimensionless number reflects the relative influence of inertial to...
2.1K
Fast Decoupled and DC Powerflow01:24

Fast Decoupled and DC Powerflow

955
The fast decoupled power flow method addresses contingencies in power system operations, such as generator outages or transmission line failures. This method provides quick power flow solutions, essential for real-time system adjustments. Fast decoupled power flow algorithms simplify the Jacobian matrix by neglecting certain elements, leading to two sets of decoupled equations:
955
Navier–Stokes Equations01:28

Navier–Stokes Equations

2.8K
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...
2.8K
Debye–Huckel–Onsager Conductance Equation01:28

Debye–Huckel–Onsager Conductance Equation

285
The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect.
285

You might also read

Related Articles

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

Sort by
Same author

Relationship Between Position, Shape, and Deformation of Papillary Muscles and Mitral Regurgitation After Transcatheter Aortic Valve Replacement.

Catheterization and cardiovascular interventions : official journal of the Society for Cardiac Angiography & Interventions·2026
Same author

A novel speckle-tracking index for predicting mortality following transcatheter aortic valve replacement.

Quantitative imaging in medicine and surgery·2026
Same author

Synthesis of Covalent Organic Frameworks and Their Applications in the Food Industry.

Journal of agricultural and food chemistry·2026
Same author

Sponge-like porous Pd-SnO<sub>2</sub> with atomic-level doping for ultrafast and stable CO detection: Synergistic effects of lattice distortion and oxygen vacancies.

Talanta·2026
Same author

Dielectric barrier discharge plasma-assisted extraction of Rhamnogalacturonan-I pectin from pomelo peel: Structural characterization and application in an emulsion gel delivery system.

Food chemistry·2026
Same author

New Insights into the Complexation of Metal Ions with Xanthate in the Flotation Process of Sulfide Minerals: A Study Based on Pyrite.

Langmuir : the ACS journal of surfaces and colloids·2026
Same journal

Agronomic Performance and Nutritive Value Evaluation of Desho Grass Varieties Under Supplementary Irrigation in Western Oromia, Ethiopia.

TheScientificWorldJournal·2026
Same journal

Physicians' and Hospital Administrators' Perspectives of Diagnosis-Related Groups (DRGs) in High-Income Countries: A Systematic Review.

TheScientificWorldJournal·2026
Same journal

The Eco-Friendly Preparation of Se, Zn, and Ag MONPs and Their Current Medical Applications and Drug Delivery for AD Diseases.

TheScientificWorldJournal·2026
Same journal

Fear of COVID-19: A Comparative Study Among University Students in Peru.

TheScientificWorldJournal·2026
Same journal

Opportunities and Challenges of Integrating Ethiopian Traditional Medicine System Into Modern Medicine: A Narrative Review.

TheScientificWorldJournal·2026
Same journal

Exploring the Antiparasitic Activity of the Sea Cucumber Isostichopus sp. aff. badionotus From the Northern Coast of Colombia Against Trypanosoma cruzi.

TheScientificWorldJournal·2026
See all related articles

Related Experiment Video

Updated: Apr 27, 2026

An Experimental and Finite Element Protocol to Investigate the Transport of Neutral and Charged Solutes across Articular Cartilage
07:57

An Experimental and Finite Element Protocol to Investigate the Transport of Neutral and Charged Solutes across Articular Cartilage

Published on: April 23, 2017

5.6K

Leapfrog/finite element method for fractional diffusion equation.

Zhengang Zhao1, Yunying Zheng2

  • 1Department of Fundamental Courses, Shanghai Customs College, Shanghai 201204, China.

Thescientificworldjournal
|June 24, 2014
PubMed
Summary
This summary is machine-generated.

This study presents a new numerical method for solving fractional diffusion equations. The leapfrog/Galerkin finite element method achieves second-order accuracy in time, confirmed by numerical examples.

More Related Videos

Lumped-Parameter and Finite Element Modeling of Heart Failure with Preserved Ejection Fraction
09:20

Lumped-Parameter and Finite Element Modeling of Heart Failure with Preserved Ejection Fraction

Published on: February 13, 2021

6.1K
A Method for Determination and Simulation of Permeability and Diffusion in a 3D Tissue Model in a Membrane Insert System for Multi-well Plates
10:33

A Method for Determination and Simulation of Permeability and Diffusion in a 3D Tissue Model in a Membrane Insert System for Multi-well Plates

Published on: February 23, 2018

27.9K

Related Experiment Videos

Last Updated: Apr 27, 2026

An Experimental and Finite Element Protocol to Investigate the Transport of Neutral and Charged Solutes across Articular Cartilage
07:57

An Experimental and Finite Element Protocol to Investigate the Transport of Neutral and Charged Solutes across Articular Cartilage

Published on: April 23, 2017

5.6K
Lumped-Parameter and Finite Element Modeling of Heart Failure with Preserved Ejection Fraction
09:20

Lumped-Parameter and Finite Element Modeling of Heart Failure with Preserved Ejection Fraction

Published on: February 13, 2021

6.1K
A Method for Determination and Simulation of Permeability and Diffusion in a 3D Tissue Model in a Membrane Insert System for Multi-well Plates
10:33

A Method for Determination and Simulation of Permeability and Diffusion in a 3D Tissue Model in a Membrane Insert System for Multi-well Plates

Published on: February 23, 2018

27.9K

Area of Science:

  • Numerical Analysis
  • Partial Differential Equations
  • Fractional Calculus

Background:

  • Fractional diffusion equations model complex phenomena.
  • Efficient numerical methods are crucial for their analysis.
  • Existing methods may have limitations in accuracy or stability.

Purpose of the Study:

  • To develop and analyze a fully discrete leapfrog/Galerkin finite element method.
  • To solve the space fractional diffusion equation accurately.
  • To establish error bounds for the proposed numerical scheme.

Main Methods:

  • Finite element method for spatial discretization.
  • Explicit leapfrog scheme for temporal discretization.
  • Analysis of generalized fractional derivative spaces in a bounded interval.

Main Results:

  • A conditionally stable, fully discrete scheme was developed.
  • An L(2)-error bound was proven, demonstrating finite element accuracy.
  • Second-order accuracy in time was achieved.

Conclusions:

  • The proposed leapfrog/Galerkin finite element method is effective for fractional diffusion equations.
  • The method offers proven accuracy and stability.
  • Numerical results validate the theoretical error analysis.