The local meshless collocation method for solving 2D fractional Klein-Kramers dynamics equation on irregular domains

Abbaszadeh, Mostafa; Pourbashash, Hossein; Oshagh, Mahmood Khaksar-e

doi:10.1108/hff-12-2020-0781

Cited by 5 publications

(2 citation statements)

References 44 publications

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“…The RBF approximations can be constructed through differentiation (DRBF) or integration (IRBF). The governing equations of fluid dynamics have been successfully solved by the DRBF- and IRBF-based methods (Mai-Duy and Tanner, 2005, 2007; Dehghan and Shokri, 2008; Kosec and Šarler, 2008, 2013; Mohebbi et al , 2014; Ngo-Cong et al , 2017; Ebrahimijahan and Dehghan, 2021; Ebrahimijahan et al , 2020, 2022a, 2022b; Abbaszadeh et al , 2022; Mesgarani et al , 2022).…”

Section: Introductionmentioning

confidence: 99%

An effective high-order five-point stencil, based on integrated-RBF approximations, for the first biharmonic equation and its applications in fluid dynamics

Mai‐Duy

Tien

Strunin

et al. 2023

HFF

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Purpose The purpose of this paper is to present a new discretisation scheme, based on equation-coupled approach and high-order five-point integrated radial basis function (IRBF) approximations, for solving the first biharmonic equation, and its applications in fluid dynamics. Design/methodology/approach The first biharmonic equation, which can be defined in a rectangular or non-rectangular domain, is replaced by two Poisson equations. The field variables are approximated on overlapping local regions of only five grid points, where the IRBF approximations are constructed to include nodal values of not only the field variables but also their second-order derivatives and higher-order ones along the grid lines. In computing the Dirichlet boundary condition for an intermediate variable, the integration constants are used to incorporate the boundary values of the first-order derivative into the boundary IRBF approximation. Findings These proposed IRBF approximations on the stencil and on the boundary enable the boundary values of the derivative to be exactly imposed, and the IRBF solution to be much more accurate and not influenced much by the RBF width. The error is reduced at a rate that is much greater than four. In fluid dynamics applications, the method is able to capture well the structure of steady highly non-linear fluid flows using relatively coarse grids. Originality/value The main contribution of this study lies in the development of an effective high-order five-point stencil based on IRBFs for solving the first biharmonic equation in a coupled set of two Poisson equations. A fast rate of convergence (up to 11) is achieved.

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Section: Introductionmentioning

confidence: 99%

An effective high-order five-point stencil, based on integrated-RBF approximations, for the first biharmonic equation and its applications in fluid dynamics

Mai‐Duy

Tien

Strunin

et al. 2023

HFF

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“…The stabilized MLS and the MLPG method are implemented in Singh and Singh (2019) for solving heat conduction problem. The main aim of Abbaszadeh et al (2022) is to propose a local meshless collocation method to solve the two-dimensional Klein-Kramers equation with a fractional derivative in the Riemann-Liouville sense. Khaksar-e Oshagh et al (2022) developed an adaptive wavelet collocation method to find more accurate numerical solution for the heat source optimal control problem.…”

Section: Introductionmentioning

confidence: 99%

Simulation of predator–prey system with two-species, two chemicals and an additional chemotactic influence via direct meshless local Petrov–Galerkin method

Abbaszadeh

Salec

Alwan

2023

HFF

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Purpose This paper aims to introduce a new numerical approach based on the local weak form and the Petrov–Galerkin idea to numerically simulation of a predator–prey system with two-species, two chemicals and an additional chemotactic influence. Design/methodology/approach In the first proceeding, the space derivatives are discretized by using the direct meshless local Petrov–Galerkin method. This generates a nonlinear algebraic system of equations. The mentioned system is solved by using the Broyden’s method which this technique is not related to compute the Jacobian matrix. Findings This current work tries to bring forward a trustworthy and flexible numerical algorithm to simulate the system of predator–prey on the nonrectangular geometries. Originality/value The proposed numerical results confirm that the numerical procedure has acceptable results for the system of partial differential equations.

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Applying thin plate splines to the Galerkin method for the numerical simulation of a nonlinear model for population dynamics

Goligerdian,

Oshagh,

Jaberi-Douraki

2024

Journal of Computational and Applied Mathematics

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The local meshless collocation method for solving 2D fractional Klein-Kramers dynamics equation on irregular domains

Cited by 5 publications

References 44 publications

An effective high-order five-point stencil, based on integrated-RBF approximations, for the first biharmonic equation and its applications in fluid dynamics

An effective high-order five-point stencil, based on integrated-RBF approximations, for the first biharmonic equation and its applications in fluid dynamics

Simulation of predator–prey system with two-species, two chemicals and an additional chemotactic influence via direct meshless local Petrov–Galerkin method

Applying thin plate splines to the Galerkin method for the numerical simulation of a nonlinear model for population dynamics

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