Numerical computation of the time non-linear fractional generalized equal width model arising in shallow water channel

Huu, Nguyen Can; Nikan, O.; Rasoulizadeh, Mohammad Navaz; Jafari, Hossein; Gasimov, Yusif S.

doi:10.2298/tsci20s1049c

Cited by 34 publications

(10 citation statements)

References 14 publications

(2 reference statements)

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“…The meshfree RBF method is used in both local and global forms. Some authors have tried localized-RBF-based strategies, such as the localized-RBF-generated FD (RBF-FD) [ 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 ] and the RBF partition of unity (RBF-PU) [ 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 ].…”

Section: Properties Of Rbfsmentioning

confidence: 99%

Determination of an Extremal in Two-Dimensional Variational Problems Based on the RBF Collocation Method

Golbabai

Safaei

Molavi-Arabshahi

2022

Entropy

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This paper introduces a direct method derived from the global radial basis function (RBF) interpolation over arbitrary collocation nodes occurring in variational problems involving functionals that depend on functions of a number of independent variables. This technique parameterizes solutions with an arbitrary RBF and transforms the two-dimensional variational problem (2DVP) into a constrained optimization problem via arbitrary collocation nodes. The advantage of this method lies in its flexibility in selecting between different RBFs for the interpolation and parameterizing a wide range of arbitrary nodal points. Arbitrary collocation points for the center of the RBFs are applied in order to reduce the constrained variation problem into one of a constrained optimization. The Lagrange multiplier technique is used to transform the optimization problem into an algebraic equation system. Three numerical examples indicate the high efficiency and accuracy of the proposed technique.

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Section: Properties Of Rbfsmentioning

confidence: 99%

Determination of an Extremal in Two-Dimensional Variational Problems Based on the RBF Collocation Method

Golbabai

Safaei

Molavi-Arabshahi

2022

Entropy

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“…[36]. In [37,38], the interpolation by radial basis function numerical method is applied to investigate the time nonlinear fractional generalized equal width model arising in shallow water channels and the regularized long-wave model arising in ion-acoustic plasma waves. The authors of [39] provide a thorough introduction to several PDE types and their solutions, as well as a number of numerical techniques with various examples.…”

Section: Introductionmentioning

confidence: 99%

On the solutions of some nonlinear fractional partial differential equations using an innovative and direct procedure

Rab,

Khan,

Tchier

et al. 2023

Phys. Scr.

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In this article, a highly effective technique is implemented to obtain the approximate solutions of strongly nonlinear fractional order partial differential equations (NFPDEs). The findings of this study show the successful behavior of the fractional novel analytical method (FNAM), which can be used successfully for the solutions of common, severe NFPDEs. In the proposed method, the nonlinearity in each mathematical model is directly handled by using fractional Taylor series, which reduces the calculation effort. In this work, the method’s strength is primarily demonstrated on NFPDEs, and the obtained results are displayed via graphs and tables. Fromthe numerical simulations, it is evident that the suggested technique has greater accuracy despite smaller calculations. It is the most straightforward method for determining the formulaic solution to any type of NFPDE and is considered to be the unique numerical methodology.

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“…In most cases, it is hard to gain analytical solutions of these problems. Therefore, numerical approaches have to be applied for approximating the solution of FDEs [5][6][7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Solving Fractional Order Differential Equations by Using Fractional Radial Basis Function Neural Network

Javadi,

Mesgarani,

Nikan

et al. 2023

Symmetry

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Fractional differential equations (FDEs) arising in engineering and other sciences describe nature sufficiently in terms of symmetry properties. This paper proposes a numerical technique to approximate ordinary fractional initial value problems by applying fractional radial basis function neural network. The fractional derivative used in the method is considered Riemann-Liouville type. This method is simple to implement and approximates the solution of any arbitrary point inside or outside the domain after training the ANN model. Finally, three examples are presented to show the validity and applicability of the method.

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Numerical computation of the time non-linear fractional generalized equal width model arising in shallow water channel

Cited by 34 publications

References 14 publications

Determination of an Extremal in Two-Dimensional Variational Problems Based on the RBF Collocation Method

Determination of an Extremal in Two-Dimensional Variational Problems Based on the RBF Collocation Method

On the solutions of some nonlinear fractional partial differential equations using an innovative and direct procedure

Solving Fractional Order Differential Equations by Using Fractional Radial Basis Function Neural Network

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