Effective approximate methods for strongly nonlinear differential equations with oscillations

2012 ◽  
Vol 6 (1) ◽  
pp. 32 ◽  
Author(s):  
Marwan Alquran ◽  
Kamel Al-Khaled
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Approximate Methods ◽  
Strongly Nonlinear

Method of Separation of Variables for the Solution of Certain Nonlinear Partial Differential Equations

1971 ◽  
Vol 93 (2) ◽  
pp. 162-164
Author(s):  
V. A. Bapat ◽  
P. Srinivasan
Keyword(s):  
Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Separation Of Variables ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Partial Differential Equation ◽  
Exact Methods ◽  
Partial Differential ◽  
Approximate Methods

A method for the solution of a certain class of nonlinear partial differential equations by the method of separation of variables is presented. The method enables the nonlinear partial differential equation to be reduced to ordinary nonlinear differential equations, which can be solved by exact methods (or by approximate methods if an exact solution is not possible).

scholarly journals Highly accurate analytical solution for free vibrations of strongly nonlinear Duffing oscillator

2021 ◽  
pp. 146134842110340
Author(s):  
Gamal Mohamed Ismail ◽  
Mahmoud Abul-Ez ◽  
Mohra Zayed ◽  
Hijaz Ahmad ◽  
Maha El-Moshneb
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Analytical Solutions ◽  
Nonlinear Differential Equations ◽  
Perturbation Technique ◽  
Duffing Oscillator ◽  
Free Vibrations ◽  
Strongly Nonlinear ◽  
Present Technique ◽  
Analytical Perturbation

Based on the suggested parameter, a new analytical perturbation technique is presented to obtain highly ordered accurate analytical solutions for nonlinear Duffing oscillator with nonlinearity of high order. Comparing the obtained results with the numerical and other previously published results reveals the usefulness and correctness of the present technique. It is shown that the results are valid for small and large amplitudes. Indeed, it is found that our proposed technique produces more accurate and computationally results than the rival known methods. The obtained results show the efficiency and capability of the present perturbation technique to be applied to various strongly nonlinear differential equations.

Mathematical modeling of building structures and nonlinear differential equations

2020 ◽  
Vol 11 (03) ◽  
pp. 2050026
Author(s):  
Victor Orlov ◽  
Yulia Zheglova
Keyword(s):  
Mathematical Modeling ◽  
Approximate Solution ◽  
Differential Equations ◽  
Numerical Experiment ◽  
Initial Conditions ◽  
Nonlinear Differential Equations ◽  
Singular Points ◽  
Building Structures ◽  
Approximate Methods ◽  
Analytic Domain

Nonlinear differential equations with moving singular points require emergence and development of new approximate methods of solution. In this paper, we give a solution to one of the problems of the analytical approximate method for solving nonlinear differential equations with moving singular points, and study the influence of the perturbation of the initial conditions on the analytical approximate solution in the analytic domain. Theoretical material was tested using a numerical experiment confirming its reliability. The theoretical material presented in this paper allows researchers to use nonlinear differential equations with moving singular points when designing mathematical models of building structures.

Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3347-3354 ◽  
Author(s):  
Nematollah Kadkhoda ◽  
Michal Feckan ◽  
Yasser Khalili
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Present Article ◽  
Analytical Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rational Functions ◽  
Expansion Method ◽  
Exponential Functions

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.

scholarly journals Solving nonlinear differential equations with differentiable quantum circuits

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Oleksandr Kyriienko ◽  
Annie E. Paine ◽  
Vincent E. Elfving
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Quantum Circuits
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