Sinc-Galerkin method for solving the time fractional convection–diffusion equation with variable coefficients

Chen, Li Juan; Li, MingZhu; Xu, Qiang

doi:10.1186/s13662-020-02959-5

Cited by 10 publications

(6 citation statements)

References 42 publications

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“…Since the VEM has great flexibility in the mesh partition, in our future work, we are going to investigate VEM approximation of an optimal control problem governed by fractional advection-diffusion-reaction equations ( [25][26][27]).…”

Section: Discussionmentioning

confidence: 99%

SUPG-Stabilized Virtual Element Method for Optimal Control Problem Governed by a Convection Dominated Diffusion Equation

Wang

Zhou

2021

Entropy

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In this paper, the streamline upwind/Petrov Galerkin (SUPG) stabilized virtual element method (VEM) for optimal control problem governed by a convection dominated diffusion equation is investigated. The virtual element discrete scheme is constructed based on the first-optimize-then-discretize strategy and SUPG stabilized virtual element approximation of the state equation and adjoint state equation. An a priori error estimate is derived for both the state, adjoint state, and the control. Numerical experiments are carried out to illustrate the theoretical findings.

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Section: Discussionmentioning

confidence: 99%

SUPG-Stabilized Virtual Element Method for Optimal Control Problem Governed by a Convection Dominated Diffusion Equation

Wang

Zhou

2021

Entropy

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“…where (17) gives us the local form, and the global form can be obtained by expanding the matrix Ψ [i] to Ψ by adding zeros to corresponding position in each row [41].…”

Section: Space Discretization Via Lrbf Methodsmentioning

confidence: 99%

“…Fractional-order CDEs can express physical problems more accurately as compared to ordinary CDEs. e fractionalorder CDE has applications in many phenomena such as the mass transport [17], environmental science [18], gas transport through heterogeneous soil and gas reservoirs [19], contaminant or liquid transport in complex media and heat conduction [20], and global weather production, in which an initially discontinuous profile is propagated by diffusion and convection, the latter with a speed of c [21].…”

Section: Introductionmentioning

confidence: 99%

On the Numerical Approximation of Three-Dimensional Time Fractional Convection-Diffusion Equations

Kamran

Kamal

Rahmat

et al. 2021

Mathematical Problems in Engineering

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In this paper, we present an efficient method for the numerical investigation of three-dimensional non-integer-order convection-diffusion equation (CDE) based on radial basis functions (RBFs) in localized form and Laplace transform (LT). In our numerical scheme, first we transform the given problem into Laplace space using Laplace transform. Then, the local radial basis function (LRBF) method is employed to approximate the solution of the transformed problem. Finally, we represent the solution as an integral along a smooth curve in the complex left half plane. The integral is then evaluated to high accuracy by a quadrature rule. The Laplace transform is used to avoid the classical time marching procedure. The radial basis functions are important tools for scattered data interpolation and for solving partial differential equations (PDEs) of integer and non-integer order. The LRBF and global radial basis function (GRBF) are used to produce sparse collocation matrices which resolve the issue of the sensitivity of shape parameter and ill conditioning of system matrices and reduce the computational cost. The application of Laplace transformation often leads to the solution in complex plane which cannot be generally inverted. In this work, improved Talbot’s method is utilized which is an efficient method for the numerical inversion of Laplace transform. The stability and convergence of the method are discussed. Two test problems are considered to validate the numerical scheme. The numerical results highlight the efficiency and accuracy of the proposed method.

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“…The radial basis function (RBF) method combined with a modification of the finite integration method (FIM) derived in 31 . The sinc -Galerkin method is proposed in 32 . The Sinc -Legendre collocation method proposed in 33 .…”

Section: Figure 1 Landfill Is One Of the Sources Of Groundwater Pollu...mentioning

confidence: 99%

Solution of convection-diffusion model in groundwater pollution

Rashidinia,

Momeni,

Molavi-Arabshahi

2023

Preprint

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This research involves in the development of the spectral collocation method using Bernoulli polynomials to the solution for time fractional convection-diffusion problems arising in groundwater pollution. The main aim is to develop the operational matrices as well as fractional derivative. The advantage of our approach is to orthogonalize the Bernoulli polynomials for sake of creating sparse operational matrices for derivatives in which having one sub diagonal non-zero entries only, andalso creating operational matrix for fractional derivative to obtained the diagonal matrix. Due to these, the convergence of our approach is fast with low cost computations. Discussion on the error analysis for the presented approach is given. Two test problems are considered to illustrate the effectiveness and applicability of our method. The maximum absolute error inthe computed solution compare with the existing method in the literature. The comparison shows that our method is more accurate and easy implemented

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Sinc-Galerkin method for solving the time fractional convection–diffusion equation with variable coefficients

Cited by 10 publications

References 42 publications

SUPG-Stabilized Virtual Element Method for Optimal Control Problem Governed by a Convection Dominated Diffusion Equation

SUPG-Stabilized Virtual Element Method for Optimal Control Problem Governed by a Convection Dominated Diffusion Equation

On the Numerical Approximation of Three-Dimensional Time Fractional Convection-Diffusion Equations

Solution of convection-diffusion model in groundwater pollution

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