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

Difference Equation Solution using z-Transform01:24

Difference Equation Solution using z-Transform

682
The z-transform is a powerful tool for analyzing practical discrete-time systems, often represented by linear difference equations. Solving a higher-order difference equation requires knowledge of the input signal and the initial conditions up to one term less than the order of the equation.
The z-transform facilitates handling delayed signals by shifting the signal in the z-domain, which corresponds to delaying the signal in the time domain, and advancing signals by similarly shifting in the...
682
Linear Differential Equations01:27

Linear Differential Equations

132
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...
132
Separable Differential Equations01:20

Separable Differential Equations

188
A separable differential equation is a type of first-order differential equation where the derivative dy/dx can be expressed as a product of two functions: one that depends only on x and another that depends only on y. This allows for the rearrangement of the equation so that all terms involving y are on one side, and all terms involving x are on the other. This process, known as the separation of variables, simplifies the process of solving the equation by enabling the integration of both...
188
Second Order systems II01:18

Second Order systems II

446
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
446
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

1.0K
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 from...
1.0K
Differential Equations: Problem Solving01:21

Differential Equations: Problem Solving

105
When analyzing the motion of falling objects, it is essential to consider not only the force of gravity but also the opposing force of air resistance. A practical example involves releasing a heavy test weight during a safety check on a ship. As the weight falls from rest, gravity accelerates it downward while air resistance exerts an upward force that increases with velocity. This dynamic interplay of forces is well described by differential equations, which provide a mathematical framework...
105

You might also read

Related Articles

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

Sort by
Same author

Temperature-Dependent Tethered Locomotion Behavior in the Madagascar Hissing Cockroach Using a Controlled-Environment Treadmill Platform with Exploratory Illumination Assays.

Biology·2026
Same author

Recent Progress of Nanogenerators for Green Energy Harvesting: Performance, Applications, and Challenges.

Nanomaterials (Basel, Switzerland)·2022
Same author

A Novel Collision-Free Homotopy Path Planning for Planar Robotic Arms.

Sensors (Basel, Switzerland)·2022
Same author

Comparative Study on the Quality of Microcrystalline and Epitaxial Silicon Films Produced by PECVD Using Identical SiF<sub>4</sub> Based Process Conditions.

Materials (Basel, Switzerland)·2021
Same author

Exploring a Novel Multiple-Query Resistive Grid-Based Planning Method Applied to High-DOF Robotic Manipulators.

Sensors (Basel, Switzerland)·2021
Same author

Statistical Assessment of Discrimination Capabilities of a Fractional Calculus Based Image Watermarking System for Gaussian Watermarks.

Entropy (Basel, Switzerland)·2021

Related Experiment Video

Updated: Mar 13, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

2.2K

A new multi-step technique with differential transform method for analytical solution of some nonlinear variable

Brahim Benhammouda1, Hector Vazquez-Leal2

  • 1Higher Colleges of Technology, Abu Dhabi Men's College, P.O. Box 25035, Abu Dhabi, United Arab Emirates.

Springerplus
|October 26, 2016
PubMed
Summary
This summary is machine-generated.

This study introduces a novel analytical method for solving nonlinear delay differential equations (DDEs) with variable delays. The technique simplifies complex DDEs for easier numerical treatment and improved solution accuracy.

Keywords:
Differential transformLaplace–Padé methodNonlinear variable delay differential equations

More Related Videos

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

664
Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
10:20

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules

Published on: September 5, 2019

8.9K

Related Experiment Videos

Last Updated: Mar 13, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

2.2K
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

664
Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
10:20

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules

Published on: September 5, 2019

8.9K

Area of Science:

  • Applied Mathematics
  • Numerical Analysis
  • Differential Equations

Background:

  • Nonlinear delay differential equations (DDEs) with variable delays pose significant challenges for traditional numerical and analytical methods.
  • Existing general-purpose codes often struggle to accurately solve these complex equations.

Purpose of the Study:

  • To develop a robust analytical solution for nonlinear DDEs with variable delays.
  • To present a novel method that overcomes the limitations of existing numerical and analytical approaches.

Main Methods:

  • A new method of steps is combined with the differential transform method (DTM).
  • This approach transforms DDEs into ordinary differential equations, solvable by DTM.
  • Laplace-Padé resummation is employed to enhance solution accuracy.

Main Results:

  • The proposed method effectively provides analytical solutions for nonlinear DDEs with variable delays.
  • Demonstrated efficiency through two illustrative examples.
  • The technique offers a simplified procedure adaptable to other analytical methods like homotopy perturbation method.

Conclusions:

  • The combined method of steps and DTM offers a powerful and efficient tool for solving challenging nonlinear DDEs.
  • The approach enhances solution accuracy and can be integrated with various analytical techniques.
  • This work provides a valuable advancement in the analytical treatment of DDEs.