An efficient nonpolynomial spline method for distributed order fractional subdiffusion equations

Li, Xuhao; Wong, Patricia J. Y.

doi:10.1002/mma.4938

Cited by 15 publications

(9 citation statements)

References 40 publications

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“…It is a fact that the analytical solution of a classical fractional differential equation is difficult to obtain, thus many numerical methods have been developed such as finite difference method, 13 finite element method, 14 spectral method, 15 nonpolynomial spline method, 16‐21 and other methods involving fractional‐order Lagrange polynomials, 22 Legendre‐Laguerre polynomials, 23 Genocchi hybrid functions, 24 Bernoulli wavelets, 25 to name a few. As one would expect, it is even more difficult to obtain analytical solutions of equations involving generalized fractional derivatives, and numerical treatment is more appropriate for such problems.…”

Section: Introductionmentioning

confidence: 99%

A higher order numerical scheme for generalized fractional diffusion equations

Ding

Wong

2020

Numerical Methods in Fluids

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In this article, we develop a higher order approximation for the generalized fractional derivative that includes a scale function z(t) and a weight function w(t). This is then used to solve a generalized fractional diffusion problem numerically. The stability and convergence analysis of the numerical scheme are conducted by the energy method. It is proven that the temporal convergence order is 3 and this is the best result to date. Finally, we present four examples to confirm the theoretical results.

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Section: Introductionmentioning

confidence: 99%

A higher order numerical scheme for generalized fractional diffusion equations

Ding

Wong

2020

Numerical Methods in Fluids

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“…Now (22) and (24) with initial and boundary conditions formulate a complete set of semidiscrete problem for (1). The error term l p+1 can also be defined as [25]…”

Section: Temporal Discretizationmentioning

confidence: 99%

“…Now, for the stability and convergence analysis, we are to find y p+1 ∈ H 2 0 (η) such that, for all g ∈ H 2 0 (η), Eqs. (22) and (24) give the following two relations:…”

Section: Temporal Discretizationmentioning

confidence: 99%

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Non-polynomial quintic spline for numerical solution of fourth-order time fractional partial differential equations

et al. 2019

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This paper presents a novel approach to numerical solution of a class of fourth-order time fractional partial differential equations (PDEs). The finite difference formulation has been used for temporal discretization, whereas the space discretization is achieved by means of non-polynomial quintic spline method. The proposed algorithm is proved to be stable and convergent. In order to corroborate this work, some test problems have been considered, and the computational outcomes are compared with those found in the exiting literature. It is revealed that the presented scheme is more accurate as compared to current variants on the topic.

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“…Spline collocation methods based on fifth degree polynomials were carried out by Siddiqi and Arshed [17] to solve PDE. Li and Wong [18] employed a parametric quantic spline technique for the solution of fractional sub-diffusion problem.…”

Section: Introductionmentioning

confidence: 99%

Analytical solutions to contact problem with fractional derivatives in the sense of Caputo

et al. 2020

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The current study extends the applications of the variational iteration method for the analytical solution of fractional contact problems. The problem involves Caputo sense while calculating the derivative of fractional order, we apply the Penalty function technique to transform it into a system of fractional boundary value problems coupled with a known obstacle. The variational iteration method is employed to find the series solution of fractional boundary value problem. For different values of fractional parameters, residual errors of solutions are plotted to make sure the convergence and accuracy of the solution. The reasonably accurate results show that one of the highly effective and stable methods for the solution of fractional boundary value problem is the method of variational iteration.

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An efficient nonpolynomial spline method for distributed order fractional subdiffusion equations

Cited by 15 publications

References 40 publications

A higher order numerical scheme for generalized fractional diffusion equations

A higher order numerical scheme for generalized fractional diffusion equations

Non-polynomial quintic spline for numerical solution of fourth-order time fractional partial differential equations

Analytical solutions to contact problem with fractional derivatives in the sense of Caputo

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