Numerical evaluation of fractional Tricomi-type model arising from physical problems of gas dynamics

Nikan, O.; Machado, J. A. Tenreiro; Avazzadeh, Z.; Jafari, Hossein

doi:10.1016/j.jare.2020.06.018

Cited by 36 publications

(11 citation statements)

References 34 publications

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“…If the accuracy of the established model is reliable, the model can be applied to predict the properties of unknown points in space. In this study, Kriging models [ 38 ], radial basis function (RBF) models [ 39 ], linear response surface models (RSM) [ 40 ], RSM-Quadratic, RSM-Cubic and RSM-Quartet models between process parameters, and optimization objectives, were established using the Isight platform, US [ 41 , 42 ].…”

Section: Methodsmentioning

confidence: 99%

An Effective Shrinkage Control Method for Tooth Profile Accuracy Improvement of Micro-Injection-Molded Small-Module Plastic Gears

et al. 2022

Polymers

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An effective method to control the non-linear shrinkage of micro-injection molded small-module plastic gears by combining multi-objective optimization with Moldflow simulation is proposed. The accuracy of the simulation model was verified in a micro-injection molding experiment using reference process parameters. The maximum shrinkage (Y1), volume shrinkage (Y2), addendum diameter shrinkage (Y3), and root circle diameter shrinkage (Y4) were utilized as optimization objectives to characterize the non-linear shrinkage of the studied gear. An analysis of the relationship between key process parameters and the optimization objectives was undertaken using a second-order response surface model (RSM-Quadratic). Finally, multi-objective optimization was carried out using the non-dominated sorting genetic algorithm-II (NSGA-II). The error rates for the key shrinkage dimensions were all below 2%. The simulation results showed that the gear shrinkage variables, Y1, Y2, Y3, and Y4, were reduced by 5.60%, 8.23%, 11.71%, and 11.39%, respectively. Moreover, the tooth profile inclination deviation (fHαT), the profile deviation (ffαT), and the total tooth profile deviation (FαT) were reduced by 47.57%, 23.43%, and 49.96%, respectively. Consequently, the proposed method has considerable potential for application in the high-precision and high-efficiency manufacture of small-module plastic gears.

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Section: Methodsmentioning

confidence: 99%

An Effective Shrinkage Control Method for Tooth Profile Accuracy Improvement of Micro-Injection-Molded Small-Module Plastic Gears

et al. 2022

Polymers

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“…The local RBFs have also been employed to reduce the model order. In some situations, researchers have found that the local RBF technique can produce the same degree of accuracy as the global RBF technique with a smaller mesh size [49][50][51][52][53]. Although small mesh sizes result in smaller ODE systems, the overall accuracy is maintained.…”

Section: The Rbf-fd Collocation Methodsmentioning

confidence: 99%

Solitary Wave Solutions of the Generalized Rosenau-KdV-RLW Equation

2020

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This paper investigates the solitary wave solutions of the generalized Rosenau–Korteweg-de Vries-regularized-long wave equation. This model is obtained by coupling the Rosenau–Korteweg-de Vries and Rosenau-regularized-long wave equations. The solution of the equation is approximated by a local meshless technique called radial basis function (RBF) and the finite-difference (FD) method. The association of the two techniques leads to a meshless algorithm that does not requires the linearization of the nonlinear terms. First, the partial differential equation is transformed into a system of ordinary differential equations (ODEs) using radial kernels. Then, the ODE system is solved by means of an ODE solver of higher-order. It is shown that the proposed method is stable. In order to illustrate the validity and the efficiency of the technique, five problems are tested and the results compared with those provided by other schemes.

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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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Numerical evaluation of fractional Tricomi-type model arising from physical problems of gas dynamics

Abstract: Graphical abstract

Cited by 36 publications

References 34 publications

An Effective Shrinkage Control Method for Tooth Profile Accuracy Improvement of Micro-Injection-Molded Small-Module Plastic Gears

An Effective Shrinkage Control Method for Tooth Profile Accuracy Improvement of Micro-Injection-Molded Small-Module Plastic Gears

Solitary Wave Solutions of the Generalized Rosenau-KdV-RLW Equation

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

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