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

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

171
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...
171
Second Order systems II01:18

Second Order systems II

257
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.
257
Uniform Depth Channel Flow: Problem Solving01:18

Uniform Depth Channel Flow: Problem Solving

220
To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional area (A) corresponding to the depth of flow (y), channel bottom width (B), and side slope (θ) is determined by:Next, calculate the wetted perimeter, which includes the bottom width and the sloped side lengths in contact with the water. Using the values of the cross-sectional area and the wetted perimeter, determine the hydraulic radius by...
220
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

610
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...
610
Bernoulli's Equation: Problem Solving01:16

Bernoulli's Equation: Problem Solving

1.6K
A Venturi meter is essential for measuring fluid flow rates in pipelines. It utilizes the relationship between fluid velocity and pressure described by Bernoulli's equation. When installed in a sewage system, the Venturi meter accurately determines the wastewater flow rate by measuring pressure differences.
The first step is to compute the cross-sectional areas of the pipe and the Venturi throat to analyze the pressure difference indicated by the pressure gauge. Next, the continuity equation is...
1.6K
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

197
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,...
197

You might also read

Related Articles

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

Sort by
Same author

Dynamics of non-Newtonian methanol conveying aluminium alloy over a rotating disc: consideration of variable nanoparticle radius and inter-particle spacing.

Nanotechnology·2024
Same author

Computer Simulations of EMHD Casson Nanofluid Flow of Blood through an Irregular Stenotic Permeable Artery: Application of Koo-Kleinstreuer-Li Correlations.

Nanomaterials (Basel, Switzerland)·2023
Same author

Shifted Legendre Collocation Method for the Solution of Unsteady Viscous-Ohmic Dissipative Hybrid Ferrofluid Flow over a Cylinder.

Nanomaterials (Basel, Switzerland)·2021
Same author

Association of Inflammatory Markers with Mortality in COVID-19 Infection.

Journal of the College of Physicians and Surgeons--Pakistan : JCPSP·2020
Same author

Spectral and Energy Efficient Low-Overhead Uplink and Downlink Channel Estimation for 5G Massive MIMO Systems.

Entropy (Basel, Switzerland)·2020
Same author

Endocytosis: a pivotal pathway for regulating metastasis.

British journal of cancer·2020
Same journal

Spatio-Temporal SIR Model with Robin Boundary Condition and Automatic Lockdown Policy.

International journal of applied and computational mathematics·2022
Same journal

Study of a Nonlinear System of Fractional Differential Equations with Deviated Arguments Via Adomian Decomposition Method.

International journal of applied and computational mathematics·2022
Same journal

An Efficient Numerical Scheme for Solving a Fractional-Order System of Delay Differential Equations.

International journal of applied and computational mathematics·2022
Same journal

Connectivity Concepts in Intuitionistic Fuzzy Incidence Graphs with Application.

International journal of applied and computational mathematics·2022
Same journal

Caputo Fractal Fractional Order Derivative of Soil Pollution Model Due to Industrial and Agrochemical.

International journal of applied and computational mathematics·2022
Same journal

Study of Fractional Order SEIR Epidemic Model and Effect of Vaccination on the Spread of COVID-19.

International journal of applied and computational mathematics·2022
See all related articles

Related Experiment Video

Updated: Nov 16, 2025

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

11.8K

Efficient Numerical Algorithm for the Solution of Eight Order Boundary Value Problems by Haar Wavelet Method.

Rohul Amin1, Kamal Shah2, Qasem M Al-Mdallal3

  • 1Department of Mathematics, University of Peshawar, Peshawar, 25120 Khyber Pakhtunkhwa Pakistan.

International Journal of Applied and Computational Mathematics
|March 1, 2021
PubMed
Summary
This summary is machine-generated.

The Haar technique effectively solves nonlinear and linear eight-order boundary value problems. This numerical method shows accurate convergence, validating its use for complex differential equations.

Keywords:
Boundary value problemsCollocation methodGauss elimination methodHaar wavelet

More Related Videos

Particle Image Velocimetry Investigation of Hemodynamics via Aortic Phantom
06:26

Particle Image Velocimetry Investigation of Hemodynamics via Aortic Phantom

Published on: February 25, 2022

4.6K
Visualization of Flow Field Around a Vibrating Pipeline Within an Equilibrium Scour Hole
09:37

Visualization of Flow Field Around a Vibrating Pipeline Within an Equilibrium Scour Hole

Published on: August 26, 2019

5.9K

Related Experiment Videos

Last Updated: Nov 16, 2025

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

11.8K
Particle Image Velocimetry Investigation of Hemodynamics via Aortic Phantom
06:26

Particle Image Velocimetry Investigation of Hemodynamics via Aortic Phantom

Published on: February 25, 2022

4.6K
Visualization of Flow Field Around a Vibrating Pipeline Within an Equilibrium Scour Hole
09:37

Visualization of Flow Field Around a Vibrating Pipeline Within an Equilibrium Scour Hole

Published on: August 26, 2019

5.9K

Area of Science:

  • Numerical Analysis
  • Applied Mathematics
  • Computational Science

Background:

  • Eight-order boundary value problems (BVPs) present significant challenges in both linear and nonlinear forms.
  • Accurate and efficient numerical methods are crucial for solving these complex differential equations.
  • Existing methods may have limitations in terms of accuracy, convergence, or applicability to high-order problems.

Purpose of the Study:

  • To introduce and apply the Haar technique for solving nonlinear and linear eight-order boundary value problems.
  • To approximate the eighth-order derivative using Haar functions and derive solutions through integration.
  • To validate the proposed Haar technique's accuracy and convergence properties.

Main Methods:

  • The Haar technique is employed, approximating the eighth-order derivative with Haar functions.
  • Integration processes are utilized to derive expressions for lower-order derivatives and the unknown function.
  • Three linear and two nonlinear examples from existing literature are used for verification.

Main Results:

  • The Haar technique demonstrated effective approximation for eight-order BVPs.
  • Comparisons with other numerical methods show competitive accuracy.
  • Maximum absolute and root mean square errors were analyzed against exact solutions, indicating good performance.

Conclusions:

  • The Haar technique provides a valid and convergent approach for solving eight-order linear and nonlinear BVPs.
  • The method exhibits a convergence rate close to 2, demonstrating its efficiency.
  • The study confirms the Haar technique's potential as a reliable tool in numerical solutions of high-order differential equations.