An efficient local meshless method for the equal width equation in fluid mechanics

Rasoulizadeh, Mohammad Navaz; Ebadi, M. J.; Avazzadeh, Z.; Nikan, O.

doi:10.1016/j.enganabound.2021.07.001

Cited by 32 publications

(10 citation statements)

References 47 publications

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Section: Definitionmentioning

confidence: 99%

“…Figure 2(a) provides the picture of quadratic curve with control points (0, 0), (1,5), (3,2) and α = π 4 . Figure 2(b) displays a cubic C-Bézier curve with α = π , it's control points are (0, 0), (2,5), (3,1), (4,4). Figure 2(c) presents the figure of a quadratic C-Bézier curve with control points (0, 8), (2,4), (4, 2), (6,3), (8,8) and α = 2.…”

Section: Definitionmentioning

confidence: 99%

“…The image of a cubic curve with α = 3 is in the middle; its control points are (0, 6), (1, 2), (3,4), (4,1). A quadratic H-Bézier curve with control points (0, 0), (2,4), (4, 7), (6,4), (8,1) and α = 1 is provided on the right.…”

Section: Definitionmentioning

confidence: 99%

“…Convection-diffusion equation is a kind of partial differential equations (PDEs) widely used in gas dynamics [1], fluid mechanics [2], environmental science [3], and other physical fields. Since it is usually difficult to get analytic solutions, numerical analysis plays a vital role in solving convection-diffusion equations.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Application of C-Bézier and H-Bézier basis functions to numerical solution of convection-diffusion equations

Sun

2022

Bound Value Probl

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Convection-diffusion equation is widely used to describe many engineering and physical problems. The finite element method is one of the most common tools for computing numerical solution. In 2003, Wang et al. proposed C-Bézier and H-Bézier basis functions which are not only a generalization of classical Bernstein basis functions but also have a free shape parameter bringing a lot of flexibility to geometrical modeling. In this paper, we adopt C-Bézier and H-Bézier basis functions to construct test and trial function spaces of finite element method to get numerical solution of convection-diffusion equations. Compared with Lagrange basis functions, numerical accuracy is improved by $1-3$ 1 − 3 order-of magnitudes which implies a much better approximation in simulating convection-diffusion problems. Several examples are presented to verify the feasibility and effectiveness of our method.

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Section: Definitionmentioning

confidence: 99%

Section: Definitionmentioning

confidence: 99%

Section: Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Application of C-Bézier and H-Bézier basis functions to numerical solution of convection-diffusion equations

Sun

2022

Bound Value Probl

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“…ere are many RBFs (expression of φ ) available in literature such as Multiquadric (MQ), Inverse Multiquadric (IMQ), Gaussian, in Plate spline [27][28][29][30][31][32][33][34] etc.…”

Section: Rbfs and Local Rbf-fd Approximationmentioning

confidence: 99%

Local RBF‐FD‐Based Mesh‐free Scheme for Singularly Perturbed Convection‐Diffusion‐Reaction Models with Variable Coefficients

Jiwari

Singh

2022

Journal of Mathematics

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This work analyze singularly perturbed convection-diffusion-reaction (CDR) models with two parameters and variable coefficients by developing a mesh-free scheme based on local radial basis function-finite difference (LRBF-FD) approximation. In the evolvement of the scheme, time derivative is discretized by forward finite difference. After that, LRBF-FD approximation is used for spatial discretization, and we obtained a system of linear equations. Then, the obtained linear system is solved by LU decomposition method in MATLAB. For numerical simulation, four singularly perturbed models are pondered to check the efficiency and chastity of the proposed scheme.

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Localized kernel‐based meshless method for pricing financial options underlying fractal transmission system

Nikan

Avazzadeh

Machado

2021

Math Methods in App Sciences

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The variation in the option pricing of the fractal transmission system is modelled by the time fractional Black–Scholes equation (TFBSE). This paper proposes an efficient local meshless method for the numerical simulation of the TFBSE. At the first step, a difference formula of L1 type is employed to get a semi‐discrete algorithm in the temporal variable with a accuracy of order 2 − α in the case of smooth solutions, where 0 < α ≤ 1 is the fractional‐order derivative. At the second step, a localized radial basis function finite difference is adopted to derive a full‐discrete scheme. Moreover, the unconditional stability and convergence of the proposed method are analyzed based on energy norm. The exact expressions for the weights of the first and second derivatives are used by imposing a multiquadric function generated by finite difference. The proposed technique produces linear systems with tridiagonal and diagonal matrices. Numerical experiments highlight the performance of the method.

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An efficient local meshless method for the equal width equation in fluid mechanics

Cited by 32 publications

References 47 publications

Application of C-Bézier and H-Bézier basis functions to numerical solution of convection-diffusion equations

Application of C-Bézier and H-Bézier basis functions to numerical solution of convection-diffusion equations

Local RBF‐FD‐Based Mesh‐free Scheme for Singularly Perturbed Convection‐Diffusion‐Reaction Models with Variable Coefficients

Localized kernel‐based meshless method for pricing financial options underlying fractal transmission system

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