Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivatives: a stable scheme based on spectral meshless radial point interpolation

Shivanian, Elyas; Jafarabadi, Ahmad

doi:10.1007/s00366-017-0522-1

Cited by 29 publications

(6 citation statements)

References 49 publications

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“…PSMRPI technique essentially exploits from above pseudospectral procedure which has been proved to be more efficient and reliable in some senses [58][59][60][61][62][63][64][65][66][67]. In fact, strictly conditionally positive definite (s.c.p.d) properties of the RBFs motivates us to consider basis B j as RBFs.…”

Section: Psmrpi Methodsmentioning

confidence: 99%

On the analysis of a kind of nonlinear Sobolev equation through locally applied pseudo‐spectral meshfree radial point interpolation

Abbasbandy

Shivanian

AL‐Jizani

2020

Numerical Methods Partial

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In this study, we develop an approximate formulation for two-dimensional nonlinear Sobolev problems by focusing on pseudospectral meshless radial point interpolation (PSMRPI) which is a kind of locally applied radial basis function interpolation and truthfully a meshless approach. In the PSMRPI method, the nodal points do not need to be regularly distributed and can even be quite arbitrary. It is easy to have high order derivatives of unknowns in terms of the values at nodal points by constructing operational matrices. The convergence and stability of the technique in some sense are studied via some examples to show the validity and trustworthiness of the PSMRPI technique.

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Section: Psmrpi Methodsmentioning

confidence: 99%

On the analysis of a kind of nonlinear Sobolev equation through locally applied pseudo‐spectral meshfree radial point interpolation

Abbasbandy

Shivanian

AL‐Jizani

2020

Numerical Methods Partial

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“…Applying the PSMRPI technique to the Motz problem is straightforward, we refer the readers to the papers (Shivanian, 2015b; Fatahi et al , 2016; Shivanian, 2016c; Shivanian and Jafarabadi, 2016, 2017a, b, c, 2018). In what follows, we apply PSMRPHI proposed in the previous section to the problems (1)–(3) in two dimensions.…”

Section: Application To the Motz Problemmentioning

confidence: 99%

“…Employing above pseudospectral procedure, a kind of meshless method called pseudospectral meshless radial point interpolation (PSMRPI) method has been recently extracted which is more powerful than other types of meshless methods in some senses (Fasshauer, 2007; Shivanian, 2015b, 2016c; Fatahi et al , 2016; Shivanian and Jafarabadi, 2016, 2017a, b, c, 2018; Liu et al , 2011). In fact, the crucial step is to replace basis functions B j by the RBF and enjoying the invertibility of the evaluation matrix A due to strictly positive definite and conditionally positive definite properties of the RBF.…”

Section: Introductionmentioning

confidence: 99%

Formulation of pseudospectral meshless radial point Hermit interpolation for the Motz problem and comparison to pseudospectral meshless radial point interpolation

Shivanian

2019

MMMS

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Purpose The purpose of this paper is to develop pseudospectral meshless radial point Hermit interpolation (PSMRPHI) for applying to the Motz problem. Design/methodology/approach The author aims to propose a kind of PSMRPHI method. Findings Based on the Motz problem, the author aims also to compare PSMRPHI and PSMRPI which belong to more influence type of meshless methods. Originality/value Although the PSMRPHI method has been infrequently used in applications, the author proves it is more accurate and trustworthy than the PSMRPI method.

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“…Mohebbi et al [25] adopted the compact FD method (CFDM) and radial basis function (RBF) meshless method (RMM). Zaky [26] and Shivanian et al [27] used the Legendre-Tau and the meshless singular boundary methods, respectively. Hafez et al [28] applied the Jacobi Spectral Galerkin method for the distributed TFRSE.…”

Section: Introductionmentioning

confidence: 99%

Numerical Approximation of the Fractional Rayleigh–Stokes Problem Arising in a Generalised Maxwell Fluid

et al. 2022

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This paper presents a numerical technique to approximate the Rayleigh–Stokes model for a generalised Maxwell fluid formulated in the Riemann–Liouville sense. The proposed method consists of two stages. First, the time discretization of the problem is accomplished by using the finite difference. Second, the space discretization is obtained by means of the predictor–corrector method. The unconditional stability result and convergence analysis are analysed theoretically. Numerical examples are provided to verify the feasibility and accuracy of the proposed method.

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Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivatives: a stable scheme based on spectral meshless radial point interpolation

Cited by 29 publications

References 49 publications

On the analysis of a kind of nonlinear Sobolev equation through locally applied pseudo‐spectral meshfree radial point interpolation

On the analysis of a kind of nonlinear Sobolev equation through locally applied pseudo‐spectral meshfree radial point interpolation

Formulation of pseudospectral meshless radial point Hermit interpolation for the Motz problem and comparison to pseudospectral meshless radial point interpolation

Numerical Approximation of the Fractional Rayleigh–Stokes Problem Arising in a Generalised Maxwell Fluid

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