Jove
Visualize
Contact Us

Related Concept Videos

Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

130
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
130
Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

3.5K
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.
3.5K
Elastic Curve from the Load Distribution01:16

Elastic Curve from the Load Distribution

264
The structural behavior of beams under distributed loads is critical for engineering analysis, which focuses on predicting how beams bend and react under such conditions. Different types of beams (e.g., cantilever, supported, or overhanging) behave differently under distributed load conditions.
For all beams, the analysis of the beam's reaction to distributed loads begins by understanding the relationship between a beam's load and the resulting shear forces and bending moments.
264
Application of the Linear Momentum Equation01:15

Application of the Linear Momentum Equation

177
The application of the linear momentum equation can be used to analyze the forces needed to hold a 180-degree pipe bend in place with flowing water. In this case, water flows through the bend with a constant cross-sectional area of 0.01 square meters and a flow velocity of 15 meters per second. The pressure at the entrance is 0.2 Megapascals and the pressure at the exit is 0.16 Megapascals.
The goal is to determine the force components in the x and y directions to hold the pipe in place. Since...
177
Steady, Laminar Flow Between Parallel Plates01:17

Steady, Laminar Flow Between Parallel Plates

375
Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
375
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

419
Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured...
419

You might also read

Related Articles

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

Sort by
Same author

A novel ABC fractional-order mathematical model for malaria transmission dynamics incorporating treatment-seeking behavior.

PloS one·2025
Same author

A tension spline fitted numerical scheme for singularly perturbed reaction-diffusion problem with negative shift.

BMC research notes·2023
Same author

A uniformly convergent numerical scheme for solving singularly perturbed differential equations with large spatial delay.

SN applied sciences·2022
Same author

Accurate numerical scheme for singularly perturbed parabolic delay differential equation.

BMC research notes·2021
Same author

Analysis of Atangana-Baleanu fractional-order SEAIR epidemic model with optimal control.

Advances in difference equations·2021
Same author

Extended cubic B-spline collocation method for singularly perturbed parabolic differential-difference equation arising in computational neuroscience.

International journal for numerical methods in biomedical engineering·2020
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 Experiment Video

Updated: Sep 21, 2025

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

6.3K

Linear B-spline finite element method for the generalized diffusion equation with delay.

Gemeda Tolessa Lubo1, Gemechis File Duressa2

  • 1Department of Mathematics, Wollega University, Nekemte, Ethiopia. gemedatolesa@gmail.com.

BMC Research Notes
|June 6, 2022
PubMed
Summary
This summary is machine-generated.

A new linear B-spline finite element method was developed for generalized diffusion equations with delay. This numerical method provides a stable and convergent solution, verified through experiments.

Keywords:
Finite elementGeneralized diffusion equation with delayLinear B-spline

More Related Videos

The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

8.7K
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

25.5K

Related Experiment Videos

Last Updated: Sep 21, 2025

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

6.3K
The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

8.7K
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

25.5K

Area of Science:

  • Numerical Analysis
  • Partial Differential Equations
  • Computational Mathematics

Background:

  • Generalized diffusion equations with delay present significant challenges in numerical computation.
  • Existing methods may lack stability or produce non-smooth solutions.

Purpose of the Study:

  • To develop and analyze a novel linear B-spline finite element method for solving generalized diffusion equations with delay.
  • To ensure the numerical method yields smooth, continuous solutions for accurate approximation.

Main Methods:

  • Spatial discretization using linear B-spline basis functions.
  • Temporal discretization employing the Crank-Nicolson scheme.
  • Derivation of conditions for asymptotic stability and convergence analysis.

Main Results:

  • The proposed method generates smooth, piecewise continuous numerical solutions.
  • Sufficient and necessary conditions for asymptotic stability were established.
  • Numerical experiments confirmed the method's applicability and accuracy.

Conclusions:

  • The developed linear B-spline finite element method is a stable and effective approach for generalized diffusion equations with delay.
  • The method's ability to provide smooth solutions enhances its utility for precise approximation.
  • Further numerical investigations support its practical implementation.