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Duffing equation
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This article presents the pseudospectral method to calculate numerical solutions for nonlinear Duffing differential equations on the interval [–1, 1]. This method is based on the differential matrix using the Chebyshev Gauss – Lobatto points. To find numerical solutions of the nonlinear Duffing differential equations, we have built an iterative procedure. The software is used in calculating in this study is Mathematica 10.4. The obtained results show that this method has high accuracy with very small errors.
9p
nhanchienthien
25-07-2023
4
3
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The paper shows that the approximate solution of the Van der PolDuffing system with time delay subjected to the white noise can be found by the second order stochastic averaging method. The stochastic system with time delay is transformed into the stochastic non-delay equation in Ito sense in accordance with the hypothesis that there are some slowly varying processes. Then the higher order stochastic averaging method is artfully applied to find the stationary probability density function for the system. The analytical results are verified by numerical simulation results.
11p
trinhthamhodang9
10-12-2020
17
1
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This is the main reason for introducing modified trial equation methods. This study aims to define a general representation of trial methods for solving nonlinear differential equations. The generalized trial equation method consists of the simple trial equation method, irrational trial method, and extended trial equation method as a common coverage.
8p
danhdanh27
07-01-2019
20
1
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In the paper a technique for determining the coefficients of the linearized equivalent equation based on the Fokker-Piank equation approach is presented. The investigation is then applied to Duffing and Vanderpol oscillations under a zero mean Gaussian white noise.
6p
chikychiky
01-11-2018
18
2
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In the present paper the convergence of mentioned method is proven and a condition relating coefficients of Duffing equation to provide the convergence procedure is formulated. Emphasize that the assumption of small parameters is not used in the proving. Some examples are presented to illustrate the proposed method, particularly exact solutions of some problems are compared with analytical approximate ones found by CSAM.
18p
thienthanquydu
21-10-2018
26
1
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The paper proposes an algorithm to solve a general Duffing equation, in which a process of transforming the initial equation to a resulting equation is proposed, and then the coupling successive approximation method is applied to solve the resulting equation. By using this algorithm a special physical factor and complex-valued solutions to the general Duffing equation are revealed.
19p
thienthanquydu
19-10-2018
40
1
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In the study an extension of the Bubnov-Galerkin method in terms of the equivalent linearization method is presented. It is combined with sequential linearization and nonlinear procedure to yield a new method for solving nonlinear equations which can improve the accuracy when the nonlinearity is strong. For illustration the Duffing oscillator is considered to show the effectiveness of the proposed method.
6p
thienthanquydu
17-10-2018
28
1
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In this short communication the main ideas of the method of equivalent linearization and dual conception are further extended to suggest a new technique for solving nonlinear differential equations. This technique allows improving the accuracy when the nonlinearity is strong and getting nonlinear features of responses. For illustration the Duffing oscillator is considered to demonstrate the effectiveness of the proposed technique.
4p
thienthanquydu
17-10-2018
44
0
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Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Existence and Analytic Approximation of Solutions of Duffing Type Nonlinear Integro-Differential Equation with Integral Boundary Conditions
19p
sting09
22-02-2012
49
2
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Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Three Solutions for Forced Duffing-Type Equations with Damping Term
11p
sting05
09-02-2012
51
5
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Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : On nonlocal three-point boundary value problems of Duffing equation with mixed nonlinear forcing terms
11p
dauphong11
06-02-2012
33
2
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