Numerical solution of the static beam problem by Bernoulli collocation method

Ren, Qingwen; Tian, Hua

doi:10.1016/j.apm.2016.05.018

Cited by 19 publications

(9 citation statements)

References 32 publications

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“…where a 4 = 0, b = 0, d = 0. Putting Equations (12)- (14) into Equation (10), it gives a system of algebraic equations of F. With the help of powerful computational programs, we get the following coefficients and solutions. Case 1.1.…”

Section: Implementation Of the Bsefmmentioning

confidence: 99%

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Extraction Complex Properties of the Nonlinear Modified Alpha Equation

Baskonus

Ercan

2021

Fractal Fract

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This paper applies one of the special cases of auxiliary method, which is named as the Bernoulli sub-equation function method, to the nonlinear modified alpha equation. The characteristic properties of these solutions, such as complex and soliton solutions, are extracted. Moreover, the strain conditions of solutions are also reported in detail. Observing the figures plotted by considering various values of parameters of these solutions confirms the effectiveness of the approximation method used for the governing model.

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Section: Implementation Of the Bsefmmentioning

confidence: 99%

“…Ordokhani et al have defined an original rational relation based on the Bernoulli wavelet [13]. Tian et al have worked on the solution of beam problem by using an ansatz method based on the Bernoulli polinomials [14], and so on [15][16][17][18][19][20][21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Extraction Complex Properties of the Nonlinear Modified Alpha Equation

Baskonus

Ercan

2021

Fractal Fract

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“…Maleknejad et al [21] used Bernstein operational matrices to obtain the numerical solution of non-linear Volterra-Fredholm-Hammerstein integral equations. Legendre polynomials are orthogonal, and their weight function is uncomplicated compared to the other orthogonal polynomials, such as Chebyshev polynomial [22], Bernoulli polynomial [23] and so on. In this paper, an algorithm based on the Bernstein and Legendre polynomials is proposed to combine the advantages of these two polynomials.…”

Section: Introductionmentioning

confidence: 99%

Numerical Analysis of Viscoelastic Rotating Beam with Variable Fractional Order Model Using Shifted Bernstein–Legendre Polynomial Collocation Algorithm

et al. 2021

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This paper applies a numerical method of polynomial function approximation to the numerical analysis of variable fractional order viscoelastic rotating beam. First, the governing equation of the viscoelastic rotating beam is established based on the variable fractional model of the viscoelastic material. Second, shifted Bernstein polynomials and Legendre polynomials are used as basis functions to approximate the governing equation and the original equation is converted to matrix product form. Based on the configuration method, the matrix equation is further transformed into algebraic equations and numerical solutions of the governing equation are obtained directly in the time domain. Finally, the efficiency of the proposed algorithm is proved by analyzing the numerical solutions of the displacement of rotating beam under different loads.

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“…The existence and multiplicity of solutions for (1.1) and its multi-dimensional case have been studied by several authors, see [5][6][7][8][9][10][11][12] and the references there in. Meanwhile, numerical methods of (1.1) have been developed in [13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Existence and uniqueness of positive solutions for Kirchhoff type beam equations

Wang¹

2020

Preprint

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This paper is concerned with the existence and uniqueness of positive solution for the fourth order Kirchhoff type problemwhere a > 0, b ≥ 0 are constants, λ ∈ R is a parameter. For the case f (u) ≡ u, we use an argument based on the linear eigenvalue problems of fourth order equations and their properties to show that there exists a unique positive solution for all λ > λ 1,a , here λ 1,a is the first eigenvalue of the above problem with b = 0; For the case f is sublinear, we prove that there exists a unique positive solution for all λ > 0 and no positive solution for λ < 0 by using bifurcation method.

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Numerical solution of the static beam problem by Bernoulli collocation method

Cited by 19 publications

References 32 publications

Extraction Complex Properties of the Nonlinear Modified Alpha Equation

Extraction Complex Properties of the Nonlinear Modified Alpha Equation

Numerical Analysis of Viscoelastic Rotating Beam with Variable Fractional Order Model Using Shifted Bernstein–Legendre Polynomial Collocation Algorithm

Existence and uniqueness of positive solutions for Kirchhoff type beam equations

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