Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Second Order systems II

Second Order systems II

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.

Linear Approximation in Time Domain

Linear Approximation in Time Domain

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,...

Second Derivatives and Laplace Operator

Second Derivatives and Laplace Operator

The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
Consider a scalar function. The curl of its...

Routh-Hurwitz Criterion II

Routh-Hurwitz Criterion II

In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...

Poisson's And Laplace's Equation

Poisson's And Laplace's Equation

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.

Relation between Mathematical Equations and Block Diagrams

Relation between Mathematical Equations and Block Diagrams

In a spring-mass-damper system, the second-order differential equation describes the dynamic behavior of the system. When transformed into the Laplace domain under zero initial conditions, this equation can be effectively analyzed and manipulated. The transformation into the Laplace domain converts differential equations into algebraic equations, simplifying the process of isolating the output.

You might also read

Related Articles

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

Sort by

Same author

Mathematical modeling and neural network based fitting of HIV/AIDS data in the workingclass population case study from Ethiopia.

Scientific reports·2025

Same author

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

PloS one·2025

Same author

Cubic non-polynomial spline on piecewise mesh for singularly perturbed reaction differential equations with robin type boundary conditions.

BMC research notes·2025

Same author

Parameter uniform finite difference formulation with oscillation free for solving singularly perturbed delay parabolic differential equation via exponential spline.

BMC research notes·2025

Same author

Exponentially fitted non-polynomial cubic spline method for time-fractional singularly perturbed convection-diffusion problems involving large temporal lag.

BMC research notes·2024

Same author

Gaussian quadrature method with exponential fitting factor for two-parameter singularly perturbed parabolic problem.

BMC research notes·2024

Search research articles

Related Experiment Video

Updated: Sep 2, 2025

Accurate Determination of the Equilibrium Surface Tension Values with Area Perturbation Tests

Accurate Determination of the Equilibrium Surface Tension Values with Area Perturbation Tests

Published on: August 30, 2019

Second-order robust finite difference method for singularly perturbed Burgers' equation.

Masho Jima Kabeto¹, Gemechis File Duressa¹

¹Department of Mathematics, Jimma University, Jimma, Ethiopia.

|August 5, 2022

Summary

This summary is machine-generated.

A new robust numerical method accurately solves singularly perturbed Burgers

Keywords:

Accurate solution Burgers' equation Singularly perturbed

More Related Videos

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Related Experiment Videos

Last Updated: Sep 2, 2025

Accurate Determination of the Equilibrium Surface Tension Values with Area Perturbation Tests

Accurate Determination of the Equilibrium Surface Tension Values with Area Perturbation Tests

Published on: August 30, 2019

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Area of Science:

Computational Mathematics
Numerical Analysis
Partial Differential Equations

Background:

Singularly perturbed Burgers' equation presents significant challenges in numerical computation.
Existing methods often struggle with accuracy and convergence for these problems.

Purpose of the Study:

To develop and present a novel second-order robust numerical method.
To enhance the accuracy and efficiency of solving singularly perturbed Burgers' equation.

Main Methods:

Application of the quasilinearization technique prior to scheme formulation.
Development of a second-order robust numerical scheme.

Main Results:

The proposed method demonstrates superior numerical accuracy.
Enhanced convergence rates compared to existing literature methods.
Provides an efficient and accurate solution for the target equation.

Conclusions:

The presented second-order robust method is effective for singularly perturbed Burgers' equation.
The method offers a significant improvement over existing numerical techniques.
It is a reliable tool for accurate and efficient computation.