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Approximate Solutions for the Nonlinear Third-Order Ordinary Differential Equations

  • M.M. Fatih Karahan EMAIL logo
Published/Copyright: May 8, 2017
Zeitschrift für Naturforschung A
From the journal Zeitschrift für Naturforschung A Volume 72 Issue 6

Abstract

A new perturbation method, multiple scales Lindstedt–Poincare (MSLP) is applied to jerk equations with cubic nonlinearities. Three different jerk equations are investigated. Approximate analytical solutions and periods are obtained using MSLP method. Both approximate analytical solutions and periods are contrasted with numerical and exact results. For the case of strong nonlinearities, obtained results are in good agreement with numerical and exact ones.

Keywords: Approximate Analytical Solutions; Multiple Scales Lindstedt–Poincare (MSLP) Method; Nonlinear Third-Order Ordinary Differential Equations; Perturbation Methods; Strongly Nonlinear Systems

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Received: 2016-12-30
Accepted: 2017-4-6
Published Online: 2017-5-8
Published in Print: 2017-5-24

©2017 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/zna-2016-0502
Keywords for this article
Approximate Analytical Solutions; Multiple Scales Lindstedt–Poincare (MSLP) Method; Nonlinear Third-Order Ordinary Differential Equations; Perturbation Methods; Strongly Nonlinear Systems

Articles in the same Issue

  1. Frontmatter
  2. Review Article
  3. Gravity beyond Einstein? Part I: Physics and the Trouble with Experiments
  4. Research Articles
  5. Mechanical, Dynamical and Thermodynamic Properties of Al-3wt%Mg from First Principles
  6. Gas Bubbles and Slugs Crossover in Air–Water Two-phase Flow by Multifractals
  7. Feinberg-Horodecki Equation with Pöschl-Teller Potential: Space-like Coherent States
  8. Approximate Solutions for the Nonlinear Third-Order Ordinary Differential Equations
  9. On Topological Indices of Certain Dendrimer Structures
  10. Increased Malleability in Tetragonal Zrx Ti1−x O2 Ternary Alloys: First-Principles Approach
  11. Generalised Multiplicative Indices of Polycyclic Aromatic Hydrocarbons and Benzenoid Systems
  12. Effect of Gravomagnetism on the Trajectory of Light Ray
  13. Rapid Communication
  14. Maximum on the Electrical Conductivity Polytherm of Molten TeCl4
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