Two high-order numerical algorithms for solving the multi-term time fractional diffusion-wave equations

Dehghan, Mehdi; Safarpoor, Mansour; Abbaszadeh, Mostafa

doi:10.1016/j.cam.2015.04.037

Cited by 132 publications

(53 citation statements)

References 60 publications

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“…The main idea of [71] is to prove estimates for the partial derivatives of the solution to a time-fractional diffusion equation posed over a bounded spatial domain. Also more research works on fractional partial differential equations can be seen in [14,2].…”

Section: A Brief Review Of Some Numerical Methods For Solving Fpdementioning

confidence: 98%

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Analysis of two methods based on Galerkin weak form for fractional diffusion-wave: Meshless interpolating element free Galerkin (IEFG) and finite element methods

Dehghan

Abbaszadeh

Mohebbi

2016

Engineering Analysis with Boundary Elements

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Section: A Brief Review Of Some Numerical Methods For Solving Fpdementioning

confidence: 98%

“…So many authors have resorted to numerical solution strategies based on convergence and stability analysis [13,14,15,16,17,18].…”

Section: Introductionmentioning

confidence: 99%

Analysis of two methods based on Galerkin weak form for fractional diffusion-wave: Meshless interpolating element free Galerkin (IEFG) and finite element methods

Dehghan

Abbaszadeh

Mohebbi

2016

Engineering Analysis with Boundary Elements

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“…Moreover, the condition numbers of coefficient matrix obtained by GLLB is smaller than those of GLL. For the multi‐term time fractional diffusion‐wave equations with Dirichlet boundary conditions, and derived only

(3 - α)

‐order temporal accuracy which is lower than second‐order. We transform the equation into its equivalent integro‐differential form and derive second‐order temporal accuracy by employing the weighted difference operators to discretize the fractional derivative and integral.…”

Section: Introductionmentioning

confidence: 99%

Gauss‐Lobatto‐Legendre‐Birkhoff pseudospectral approximations for the multi‐term time fractional diffusion‐wave equation with Neumann boundaryconditions

Liu

Lü

2018

Numerical Methods Partial

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A second‐order finite difference/pseudospectral scheme is proposed for numerical approximation of multi‐term time fractional diffusion‐wave equation with Neumann boundary conditions. The scheme is based upon the weighted and shifted Grünwald difference operators approximation of the time fractional calculus and Gauss‐Lobatto‐Legendre‐Birkhoff (GLLB) pseudospectral method for spatial discretization. The unconditionally stability and convergence of the scheme are rigorously proved. Numerical examples are carried out to verify theoretical results.

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“…The authors of presented the FDMs for numerically solving the fractional Klein–Kramers equation. We also refer the interested readers to and the references therein to see some research works that have used FDMs to solve FPDEs.…”

Section: Introductionmentioning

confidence: 99%

The dual reciprocity boundary elements method for the linear and nonlinear two‐dimensional time‐fractional partial differential equations

Dehghan

Safarpoor

2016

Math Methods in App Sciences

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In this paper, we apply the dual reciprocity boundary elements method for the numerical solution of two-dimensional linear and nonlinear time-fractional modified anomalous subdiffusion equations and time-fractional convection-diffusion equation. The fractional derivative of problems is described in the Riemann-Liouville and Caputo senses. We employ the linear radial basis function for interpolation of the nonlinear, inhomogeneous and time derivative terms. This method is improved by using a predictor-corrector scheme to overcome the nonlinearity which appears in the nonlinear problems under consideration. The accuracy and efficiency of the proposed schemes are checked by five test problems. The proposed method is employed for solving some examples in two dimensions on unit square and also in complex regions to demonstrate the efficiency of the new technique.

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Two high-order numerical algorithms for solving the multi-term time fractional diffusion-wave equations

Cited by 132 publications

References 60 publications

Analysis of two methods based on Galerkin weak form for fractional diffusion-wave: Meshless interpolating element free Galerkin (IEFG) and finite element methods

Analysis of two methods based on Galerkin weak form for fractional diffusion-wave: Meshless interpolating element free Galerkin (IEFG) and finite element methods

Gauss‐Lobatto‐Legendre‐Birkhoff pseudospectral approximations for the multi‐term time fractional diffusion‐wave equation with Neumann boundaryconditions

The dual reciprocity boundary elements method for the linear and nonlinear two‐dimensional time‐fractional partial differential equations

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