Numerical solution of large deflection beams by using the Laplace Adomian decomposition method

Lin, Ming-Xian; Tseng, Chia-Hsiang; Chen, Cha'o. Kuang

doi:10.1108/ec-01-2021-0044

Cited by 4 publications

(3 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The PHI-four equation has been studied in earlier research to provide the analytical and numerical solutions by using Adomian decomposition method [4], Sumudu transform method and Homotopy perturbation method [5][6][7], asymptotic iteration method [8], fourth order compact and conservative scheme [9], orthogonal spectral collocation scheme [10] based on Jacobi envelopes, Soliton of solitary wave using Anstaz technique [11], first integral method [12], modified extended direct algebraic method [13], natural decomposition method [14], bifurcation analysis and Anstaz method [15], variational iteration method [16], He's method [17] and others. For instances, recently LADT has been successfully implemented in a variety of differential model like; SDIQR model of Covid-19 [18], Lane emden differential equation [19], model of lassa diseases [20], numerical solution of large deflection beam [21], simulation of unsteady MHD flow in incompressible fluid [22], approximation of time fractional advection dispersion equation [23], approximate solution of fractional order sterile insect technology model [24] etc. Similarly various integral transforms [25,26] are implemented to solve higher order partial differential equations.…”

Section: Introductionmentioning

confidence: 99%

The kink-antikink single waves in dispersion systems by generalized PHI-four equation in mathematical physics

Sahu,

Jena

2024

Phys. Scr.

View full text Add to dashboard Cite

An essential aspect of mathematical physics is the PHI-four equation, which is a specific version of the Klein-Gordon equation that predicts particle physics phenomena. The present paper addresses numerical approaches to generalized PHI-four equation based on Laplace Adomian Decomposition Technique (LADT) which is governed by coupling of Laplace transform and Adomian decomposition method to determine the kink-antikink single waves in dispersion systems arises in mathematical physics. The nonlinear terms in the PHI-four equation are handled using the accelerated polynomial i.e., Adomian polynomial. The approach is extremely interesting computationally and is straightforward to execute. The accuracy and robustness of the current scheme are demonstrated by four test problems. To demonstrate the efficacy of our suggested approach, the current result is contrasted with both the analytical solution and existing solutions in literature. Stability and convergence analysis are well developed to justify the applicability of the current approach.

show abstract

Section: Introductionmentioning

confidence: 99%

The kink-antikink single waves in dispersion systems by generalized PHI-four equation in mathematical physics

Sahu,

Jena

2024

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…The formulas to obtain these polynomials were developed by Adomian [1][2][3][4]. In recent years, more and more researchers have applied this method to solving nonlinear systems [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. We firstly study the algorithm and convergence analysis of ADM, and then apply ADM to constructing approximate solutions for nonlinear equations with initial data, including algebraic equations, fractional ordinary differential equations and fractional partial differential equations.…”

Section: Introductionmentioning

confidence: 99%

Kesir mertebeden rastgele adi diferansiyel denklemlerin Adomian Ayrıştırma Yöntemi ile analizi

MERDAN,

ATASOY

2024

Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi

View full text Add to dashboard Cite

In this study, random ordinary differential equations obtained by randomly choosing the coefficients or initial conditions of the ordinary differential equations will be analyzed by the Adomian Decomposition Method. The initial conditions or coefficients of the equations will be converted to random variables with normal and exponential distribution. Probability characteristics such as expected value, variance and confidence interval of the obtained random ordinary differential equations will be calculated. Obtained results will be drawn with the help of MATLAB (2013a) package program and random results will be interpreted.

show abstract

“…The proposed approach found the solution without linearization or discretization process. Lin et al 38 used the Laplace Adomian decomposition method for investigating the deformation and nonlinear behavior of the large deflection problems on the Euler–Bernoulli beam. The validity of the LADM has been confirmed by comparing the numerical results to different methods.…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of non-uniform Bernoulli beam by using Laplace Adomian decomposition method

Lin

Deng

Chen

2022

Proceedings of the Institution of Mechanical Engineers, Part C:

Self Cite

View full text Add to dashboard Cite

This paper discusses an investigation into the influence of the cone ratio and axial force on the vibration problem in a non-uniform cantilever Euler–Bernoulli beam. In the analysis, the governing equation for the non-uniform cantilever Euler–Bernoulli beam is solved using the Laplace Adomian decomposition method (LADM). The LADM is used to convert the governing equation into a characteristic equation of a non-uniform Euler–Bernoulli beam, and a simple calculation is performed to obtain the natural frequencies and corresponding modals. The obtained numerical results are verified using a comparison with the results reported in previous studies. The present study speeds up the convergent rate and the accuracy of calculation by comparing the results using the modified Adomian decomposition method (MADM) and differential transformation method (DTM). The main power and advantage of the LADM are providing an analytical approximation to a nonlinear differential equation without linearization, perturbation, approximation, and discretization, all of which lead to huge numerical computation. The numerical methods demonstrated that the natural frequency increases with increasing the rotating spring modulus and moving spring modulus, and the moving spring modulus has a greater influence on the natural frequency. The effects of the cone ratio and axial force are presented for non-uniform Euler–Bernoulli beams. The numerical results show that the LADM is a suitable technique for analyzing the behavioral characteristics of beams.

show abstract

Numerical solution of large deflection beams by using the Laplace Adomian decomposition method

Cited by 4 publications

References 33 publications

The kink-antikink single waves in dispersion systems by generalized PHI-four equation in mathematical physics

The kink-antikink single waves in dispersion systems by generalized PHI-four equation in mathematical physics

Kesir mertebeden rastgele adi diferansiyel denklemlerin Adomian Ayrıştırma Yöntemi ile analizi

Free vibration analysis of non-uniform Bernoulli beam by using Laplace Adomian decomposition method

Contact Info

Product

Resources

About