An alternating direction implicit legendre spectral method for simulating a 2D multi-term time-fractional Oldroyd-B fluid type diffusion equation

Liu, Yanqin; Yin, Xiuling; Liu, Fawang; Xin, Xiaoyi; Shen, Yanfeng; Feng, Libo

doi:10.1016/j.camwa.2022.03.020

Cited by 9 publications

(4 citation statements)

References 36 publications

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“…The spectral tau, Galerkin, and collocation schemes are three well-known types of spectral techniques. Because the spectral collocation method provides good approximations to differential equations and integral equations in physical space, [50][51][52][53][54][55][56][57][58][59][60][61] it can be adapted and implemented to various problems, including variable coefficient and nonlinear partial differential equations. We start our numerical scheme by splitting the complex functions into their imaginary and real parts:…”

Section: The Numerical Schemementioning

confidence: 99%

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Tanh Jacobi spectral collocation method for the numerical simulation of nonlinear Schrödinger equations on unbounded domain

Mostafa

Zaky

Hafez

et al. 2022

Math Methods in App Sciences

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We present a class of orthogonal functions on infinite domain based on Jacobi polynomials. These functions are generated by applying a tanh transformation to Jacobi polynomials. We construct interpolation and projection error estimates using weighted pseudo‐derivatives tailored to the involved mapping. Then, using the nodes of the newly introduced tanh Jacobi functions, we develop an efficient spectral tanh Jacobi collocation method for the numerical simulation of nonlinear Schrödinger equations on the infinite domain without using artificial boundary conditions. The applicability and accuracy of the solution method are demonstrated by two numerical examples for solving the nonlinear Schrödinger equation and the nonlinear Ginzburg–Landau equation.

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Section: The Numerical Schemementioning

confidence: 99%

“…consequently, the estimate (48) follows directly from ( 53), (54), and (47). Next, in order to prove (49), we recall the Gamma function's property:…”

Section: Orthogonal Projectionsmentioning

confidence: 99%

Tanh Jacobi spectral collocation method for the numerical simulation of nonlinear Schrödinger equations on unbounded domain

Mostafa

Zaky

Hafez

et al. 2022

Math Methods in App Sciences

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“…Hendy and Zaky [15] proposed a spectral method for a coupled system of nonlinear multi-term time-space fractional diffusion equations by using the L1 formula on a time-graded mesh. Liu et al [16] developed an ADI Legendre spectral method for solving a multi-term time-fractional Oldroyd-B fluid-type diffusion equation. Wei and Wang [17] constructed a higher-order numerical scheme for the multi-term variable-order time-fractional diffusion equation by using the local discontinuous Galerkin method.…”

Section: Introductionmentioning

confidence: 99%

A Mixed Finite Element Method for the Multi-Term Time-Fractional Reaction–Diffusion Equations

Zhao,

Dong,

Fang

2024

Fractal Fract

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In this work, a fully discrete mixed finite element (MFE) scheme is designed to solve the multi-term time-fractional reaction–diffusion equations with variable coefficients by using the well-known L1 formula and the Raviart–Thomas MFE space. The existence and uniqueness of the discrete solution is proved by using the matrix theory, and the unconditional stability is also discussed in detail. By introducing the mixed elliptic projection, the error estimates for the unknown variable u in the discrete L∞(L2(Ω)) norm and for the auxiliary variable λ in the discrete L∞((L2(Ω))2) and L∞(H(div,Ω)) norms are obtained. Finally, three numerical examples are given to demonstrate the theoretical results.

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“…Researchers have studied the impact of these fluids on real‐world phenomena, for example, Liu et al. [20] used numerical analysis to investigate the influence of generalized OBF. Other important applications of the OBF model can be found in references [21–23].…”

Section: Introductionmentioning

confidence: 99%

Analysis of constant proportional Caputo operator on the unsteady Oldroyd‐B fluid flow with Newtonian heating and non‐uniform temperature

Arif,

Kumam,

Watthayu

2023

Z Angew Math Mech

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The Caputo operator has recently gained popularity as a widely used operator in fractional calculus. The purpose of this current research is to develop a new operator by combining the Caputo and proportional derivatives, resulting in the constant proportional Caputo (CPC) fractional operator. To demonstrate the dynamic behavior of this newly defined operator, it was applied to the unsteady Oldroyd‐B fluid model. Additionally, the research considered an Oldroyd‐B fluid in a generalized Darcy medium, considering non‐uniform temperature, radiation, and heat generation. Analytical solutions for the proposed model were obtained and presented in graphical form using the computational software MATHCAD. The impact of various physical parameters was also examined through graphical analysis of velocity and temperature profiles, as well as a comparison between isothermal and non‐uniform temperature. In conclusion, this research found that the CPC fractional operator effectively explains the dynamics of the Oldroyd‐B fluid model with stable and strong memory effects, compared to the classical model.

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An alternating direction implicit legendre spectral method for simulating a 2D multi-term time-fractional Oldroyd-B fluid type diffusion equation

Cited by 9 publications

References 36 publications

Tanh Jacobi spectral collocation method for the numerical simulation of nonlinear Schrödinger equations on unbounded domain

Tanh Jacobi spectral collocation method for the numerical simulation of nonlinear Schrödinger equations on unbounded domain

A Mixed Finite Element Method for the Multi-Term Time-Fractional Reaction–Diffusion Equations

Analysis of constant proportional Caputo operator on the unsteady Oldroyd‐B fluid flow with Newtonian heating and non‐uniform temperature

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