An Accurate Analytical Solution to Strongly Nonlinear Differential Equations

2020 ◽  
Vol 14 (1) ◽  
pp. 141-149 ◽  
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Strongly Nonlinear

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.

scholarly journals Analytical solution of Velocities and Temperature fields using Homotopy Analysis Method

2021 ◽  
Vol 12 (1S) ◽  
pp. 691-700
Author(s):  
Dr. K.V.Tamil Selvi , Et. al.
Keyword(s):  
Partial Differential Equations ◽  
Analytical Solution ◽  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Nonlinear Differential Equations ◽  
Temperature Fields ◽  
Analysis Method ◽  
Partial Differential ◽  
Convective Boundary ◽  
Homotopy Analysis

In this paper, analysis of nonlinear partial differential equations on velocities and temperature with convective boundary conditions are investigated. The governing partial differential equations are transformed into ordinary differential equations by applying similarity transformations. The system of nonlinear differential equations are solved using Homotopy Analysis Method (HAM). An analytical solution is obtained for the values of Magnetic parameter M2, Prandtl number Pr, Porosity parameter

scholarly journals Analytical solution of a class of nonlinear differential equations of the third order in the complex area

2021 ◽  
pp. 75-84
Author(s):  
Виктор Николаевич Орлов ◽  
Людмила Витальевна Мустафина
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
A Priori Estimates ◽  
Nonlinear Differential Equations ◽  
A Priori ◽  
A Priori Estimate ◽  
Third Order ◽  
The Third ◽  
Change Of Variables ◽  
Priori Estimates

В работе приводится доказательство теоремы существования и единственности аналитического решения класса нелинейных дифференциальных уравнений третьего порядка, правая часть которого представлена полиномом шестой степени, в комплексной области. Расширен класс рассматриваемых уравнений за счет новой замены переменных. Получена априорная оценка аналитического приближенного решения. Представлен вариант численного эксперимента оптимизации априорных оценок с помощью апостериорных. The article presents a proof of the theorem of the existence and uniqueness of the analytical solution of the class of nonlinear differential equations of the third order, with a polynomial right-hand side of the sixth degree, in the complex domain. The class of the considered equations has been extended by means of a new change of variables. An a priori estimate of the analytical approximate solution is obtained. A variant of the numerical experiment of optimizing a priori estimates using a posteriori estimates is presented.

scholarly journals Differential equations of motion of a material point in the perpendicular plane to the plane of the gravitating disk

2021 ◽  
Vol 24 (3) ◽  
pp. 1307
Author(s):  
Zhenisgul Rakhmetullina ◽  
Indira Uvaliyeva ◽  
Farida Amenova
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Nonlinear Equations ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Material Point ◽  
Point System ◽  
Disk Material ◽  
Analytical Review ◽  
Celestial Bodies

This paper presents an analytical solution of the differential equations of motion of a material point in the plane perpendicular to the plane of the gravitating disk. The differential equations of the problem under study and the applied Gilden's method are described in the works of A. Poincaré. Differential equations refer to nonlinear equations. The analysis of methods for solving nonlinear differential equations was carried out. The methodology of applying the Gilden method to the solution of the differential equations under consideration can be applied in studies of the problem of the motion of celestial bodies in the “disk-material point” system in perpendicular planes. To identify the various properties of the gravitating disk, an analytical review of the state of the problem of the motion of a material point in the field of a gravitating disk is carried out. Summing up the presented review on the problem under study, a conclusion is made. The substantive formulation of the problem is described, which is formulated as follows: the study of the influence of disk-shaped bodies on the motion of a material point and methods for their solution.

Large Deflection Analysis of Non-Hinged Arch

2013 ◽  
Vol 705 ◽  
pp. 459-462
Author(s):  
Jia Wei Zhang ◽  
Sheng Wei Liu ◽  
He Min Liu ◽  
Ting Bin Liu ◽  
Jian Chang Zhao
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Finite Deformation ◽  
Theoretical Basis ◽  
Deformation Theory ◽  
Large Deflection ◽  
Nonlinear Differential Equations ◽  
Long Span ◽  
Deflection Analysis ◽  
Finite Deformation Theory

Based on the finite deformation theory nonlinear differential equations of uniform-sectional circular arch is deduced, and analytical solution for displacement of the non-hinged arch under load is obtained. This paper provides a theoretical basis for the analysis and calculation of the long span arch.

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