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

Separable Differential Equations01:20

Separable Differential Equations

343
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...
343
Linear Differential Equations01:27

Linear Differential Equations

276
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...
276
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

501
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
501
Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

4.2K
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.
4.2K
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

435
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
435
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

1.1K
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...
1.1K

You might also read

Related Articles

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

Sort by
Same author

Numerical Investigation of the Effect of Unsteadiness on Three-Dimensional Flow of an Oldroyb-B Fluid.

PloS one·2015
Same author

The mixed finite element multigrid method for stokes equations.

TheScientificWorldJournal·2015
Same author

Geometric construction of eighth-order optimal families of Ostrowski's method.

TheScientificWorldJournal·2015
Same author

Magnetic drug targeting in a permeable microvessel.

Microvascular research·2012
Same author

Personality concomitants of loneliness among black and white male Zimbabwean adolescents.

The Journal of social psychology·1989
Same author

Towards an AIDS information strategy for Zimbabwe.

AIDS education and prevention : official publication of the International Society for AIDS Education·1989

Related Experiment Video

Updated: Apr 23, 2026

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
07:11

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

Published on: August 19, 2021

3.3K

A bivariate Chebyshev spectral collocation quasilinearization method for nonlinear evolution parabolic equations.

S S Motsa1, V M Magagula1, P Sibanda1

  • 1School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsville, Pietermaritzburg 3209, South Africa.

Thescientificworldjournal
|September 26, 2014
PubMed
Summary

A novel numerical method accurately solves complex nonlinear partial differential equations (NPDEs). This approach combines quasilinearization and spectral methods, showing excellent agreement with exact solutions for various evolution 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

703
Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

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

10.3K

Related Experiment Videos

Last Updated: Apr 23, 2026

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
07:11

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

Published on: August 19, 2021

3.3K
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

703
Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

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

10.3K

Area of Science:

  • Applied Mathematics
  • Numerical Analysis
  • Computational Physics

Background:

  • Higher-order nonlinear evolution partial differential equations (NPDEs) model complex phenomena in physics and biology.
  • Existing analytical methods are often insufficient for these complex equations.

Purpose of the Study:

  • To introduce and validate a new hybrid numerical method for solving higher-order NPDEs.
  • To demonstrate the method's accuracy, convergence, and effectiveness on benchmark nonlinear evolution equations.

Main Methods:

  • The proposed method integrates quasilinearization with the Chebyshev spectral collocation method.
  • Bivariate Lagrange interpolation is employed within the numerical scheme.
  • The method is applied to solve modified KdV-Burgers, highly nonlinear KdV, Fisher's, Burgers-Fisher, Burgers-Huxley, and Fitzhugh-Nagumo equations.

Main Results:

  • Numerical solutions obtained by the new method show high-order accuracy.
  • Convergence is verified through graphical analysis.
  • Error graphs demonstrate excellent agreement between numerical results and known exact analytical solutions.

Conclusions:

  • The combined quasilinearization and spectral collocation method is accurate and effective for solving higher-order NPDEs.
  • The method offers a reliable approach for analyzing complex nonlinear phenomena.
  • The study confirms the method's potential for a wide range of scientific applications.