Numerical methods based on radial basis function-generated finite difference (RBF-FD) for solution of GKdVB equation

Rashidinia, Jalil; Rasoulizadeh, Mohammad Navaz

doi:10.1016/j.wavemoti.2019.05.006

Cited by 30 publications

(12 citation statements)

References 37 publications

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“…16, and after simplifying we obtain: In the aforesaid relation by choosing θ = 1/2 and after simplifying, the inequality (Q -P) ≥ 0 holds. Consequently, it concludes that | ζ | ≤ 1 [21]. Therefore, the necessary condition for the stability is provided and we can state that our method is convergence.…”

Section: Spatial Discretization the Local Rbf In Finite Difference Modementioning

confidence: 67%

“…where ( ) The RBF interpolation method uses linear combinations of translates of one function ϕ of a single real variable [21,22]. The numerical approximation u(x i , t n ) at a point of interest x i is expanded:…”

Section: Time Discretization Strategymentioning

confidence: 99%

“…This local RBF technique can be viewed as a generalized form of the traditional FD technique, hence, it is also known as the RBF-FD technique [21,23]. For the convenience of marking, we as-…”

Section: Spatial Discretization the Local Rbf In Finite Difference Modementioning

confidence: 99%

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

et al. 2020

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The generalized equal width model is an important non-linear dispersive wave model which is naturally used to describe physical situations in a water channel. In this work, we implement the idea of the interpolation by radial basis function to obtain numerical solution of the non-linear time fractional generalized equal width model defined by Caputo sense. In this technique, firstly, a time discretization is accomplished via the finite difference approach and the non-linear term is linearized by a linearization method. Afterwards, with the help of the radial basis function approximation method is used to discretize the spatial derivative terms. The stability of the method is theoretically discussed using the von Neumann (Fourier series) method. Numerical results and comparisons are presented which illustrate the validity and accuracy of our proposed concepts.

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Section: Spatial Discretization the Local Rbf In Finite Difference Modementioning

confidence: 67%

Section: Time Discretization Strategymentioning

confidence: 99%

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

et al. 2020

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“…. , M) of weak classifier S4VM; (6) Using the weight distribution β m , calculate the m th weak classifier G m ; 7Update the weight distribution of the training set w m+1,i ; (8) m � m + 1; (9) else (10) jump out of the loop; (11) end (12) end for (13) According to formula (11), m groups of weak classifiers are linearly combined, and the final classifier is output; (14) Use the final classifier to predict the training set classification. ALGORITHM 2: AdaBoost-ISSA-S4VM classification model algorithm.…”

Section: Comparison On Benchmark Functions With Hybridmentioning

confidence: 99%

“…Rasoulizadeh et al [13] modified local RBF-generated finite difference method (RBF-FD) based on local stencil nodes which has a sparsity system to overcame the dense and ill-condition. Rashidinia et al [14] also has proposed the two meshless collocation methods based on radial basis function-generated finite difference (RBF-FD) and global RBF(GRBF) methods, and the simulation results have shown that the proposed approach was viable and effective. Can et al [15] modified the idea of the interpolation by radial basis function, and the obtained results show that the proposed method is able to provide valid and accurate results and outperform other counterparts.…”

Section: Introductionmentioning

confidence: 99%

Semi-Supervised Ensemble Classifier with Improved Sparrow Search Algorithm and Its Application in Pulmonary Nodule Detection

Zhang

Xia

et al. 2021

Mathematical Problems in Engineering

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The Adaptive Boosting (AdaBoost) classifier is a widely used ensemble learning framework, and it can get good classification results on general datasets. However, it is challenging to apply the AdaBoost classifier directly to pulmonary nodule detection of labeled and unlabeled lung CT images since there are still some drawbacks to ensemble learning method. Therefore, to solve the labeled and unlabeled data classification problem, the semi-supervised AdaBoost classifier using an improved sparrow search algorithm (AdaBoost-ISSA-S4VM) was established. Firstly, AdaBoost classifier is used to construct a strong semi-supervised classifier using several weak classifiers S4VM (AdaBoost-S4VM). Next, in order to solve the accuracy problem of AdaBoost-S4VM, sparrow search algorithm (SSA) is introduced in the AdaBoost classifier and S4VM. Then, sine cosine algorithm and new labor cooperation structure are adopted to increase the global optimal solution and convergence performance of sparrow search algorithm, respectively. Furthermore, based on the improved sparrow search algorithm and adaptive boosting classifier, the AdaBoost-S4VM classifier is improved. Finally, the effective improved AdaBoost-ISSA-S4VM classification model was developed for actual pulmonary nodule detection based on the publicly available LIDC-IDRI database. The experimental results have proved that the established AdaBoost-ISSA-S4VM classification model has good performance on labeled and unlabeled lung CT images.

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A second order convergent difference scheme for the initial‐boundary value problem of Korteweg–de Vires equation

Wang

Sun

2020

Numerical Methods Partial

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In this article, we present a two-level implicit difference scheme for Korteweg-de Vires equation with the initial and boundary conditions by the method of order reduction. The truncation error of the difference scheme is analyzed in detail. In the practical computation, the introduced intermediate variable is decoupled in order to reduce the computational cost. It is proved that the difference scheme is solvable by the Browder theorem. The conservation, boundedness, and the unconditional convergence of the numerical solution are also analyzed at length. The convergence order is two both in space and in time in L 2 -norm. The numerical solution is proved to be unique under the optimal step ratio condition. Numerical examples demonstrate that the theoretical analysis is correct.

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Numerical methods based on radial basis function-generated finite difference (RBF-FD) for solution of GKdVB equation

Cited by 30 publications

References 37 publications

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

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

Semi-Supervised Ensemble Classifier with Improved Sparrow Search Algorithm and Its Application in Pulmonary Nodule Detection

A second order convergent difference scheme for the initial‐boundary value problem of Korteweg–de Vires equation

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