An efficient Haar wavelet collocation method for the numerical solution of multi-term fractional differential equations

Shiralashetti, S. C.; Deshi, A. B.

doi:10.1007/s11071-015-2326-4

Cited by 69 publications

(32 citation statements)

References 19 publications

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“…The fractional differential equations model areal problem in life that needs a solution. Therefore, there are many different numerical methods that solve these equations, such as the predictor‐corrector method, Legendre wavelets, Legendre spectral method, Legendre collocation method, pseudo‐spectral scheme, Haar wavelet collocation method, Chebyshev spectral methods,() other techniques,() and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of multiterm variable‐order fractional differential equations via shifted Legendre polynomials

El‐Sayed

Agarwal

2019

Math Methods in App Sciences

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In this paper, shifted Legendre polynomials will be used for constructing the numerical solution for a class of multiterm variable‐order fractional differential equations. In the proposed method, the shifted Legendre operational matrix of the fractional variable‐order derivatives will be investigated. The fundamental problem is reduced to an algebraic system of equations using the constructed matrix and the collocation technique, which can be solved numerically. The error estimate of the proposed method is investigated. Some numerical examples are presented to prove the applicability, generality, and accuracy of the suggested method.

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Section: Introductionmentioning

confidence: 99%

Numerical solution of multiterm variable‐order fractional differential equations via shifted Legendre polynomials

El‐Sayed

Agarwal

2019

Math Methods in App Sciences

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“…For the multi-term time fractional diffusion equation in bounded convex polyhedron domain, Jin et al (2015) [12] gave the numerical algorithm based on the standard Galerkin finite element method of space discretization and the finite difference method of time discretization, and discussed its stability and error estimation. Shiralashetti and Deshi (2016) [13] applied the Haar wavelet collocation method for solving multi-term fractional differential equations using the fractional order operational matrix of integration. Li et al (2018) [14], based on the mixed finite-element method and finite difference method, gave the numerical algorithms of the multi-term time-fractional diffusion equations and diffusion-wave equations with Caputo fractional derivative.…”

Section: Introductionmentioning

confidence: 99%

A New Kind of Parallel Natural Difference Method for Multi-Term Time Fractional Diffusion Model

Yang

2020

Mathematics

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Multi-term time fractional diffusion model is not only an important physical subject, but also a practical problem commonly involved in engineering. In this paper, we apply the alternating segment technique to combine the classical explicit and implicit schemes, and propose a parallel nature difference method alternating segment pure explicit-implicit (PASE-I) and alternating segment pure implicit-explicit (PASI-E) difference schemes for multi-term time fractional order diffusion equations. The existence and uniqueness of the solutions are proved, and stability and convergence analysis of the two schemes are also given. Theoretical analyses and numerical experiments show that the PASE-I and PASI-E schemes are unconditionally stable and satisfy second-order accuracy in spatial precision and 2 − α order in time precision. When the computational accuracy is equivalent, the CPU time of the two schemes are reduced by up to 2/3 compared with the classical implicit difference method. It indicates that the PASE-I and PASI-E parallel difference methods are efficient and feasible for solving multi-term time fractional diffusion equations.

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“…These are the most familiar and simple Haar wavelets. Haar wavelets are used by many researchers because of their simplicity [5][6][7][8][9][10]. The disadvantage of using Haar's functions is the low accuracy of the numerical approach.…”

Section: Introductionmentioning

confidence: 99%

Chebyshev wavelet collocation method for Ginzburg-Landau equation

Seçer

Bakir

2019

THERM SCI

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The main aim of this paper is to investigate the efficient Chebyshev wavelet collocation method for Ginzburg-Landau equation. The basic idea of this method is to have the approximation of Chebyshev wavelet series of a non-linear PDE. We demonstrate how to use the method for the numerical solution of the Ginzburg-Landau equation with initial and boundary conditions. For this purpose, we have obtained operational matrix for Chebyshev wavelets. By applying this technique in Ginzburg-Landau equation, the PDE is converted into an algebraic system of non-linear equations and this system has been solved using MAPLE computer algebra system. We demonstrate the validity and applicability of this technique which has been clarified by using an example. Exact solution is compared with an approximate solution. Moreover, Chebyshev wavelet collocation method is found to be acceptable, efficient, accurate and computational for the non-linear or PDE.

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An efficient Haar wavelet collocation method for the numerical solution of multi-term fractional differential equations

Cited by 69 publications

References 19 publications

Numerical solution of multiterm variable‐order fractional differential equations via shifted Legendre polynomials

Numerical solution of multiterm variable‐order fractional differential equations via shifted Legendre polynomials

A New Kind of Parallel Natural Difference Method for Multi-Term Time Fractional Diffusion Model

Chebyshev wavelet collocation method for Ginzburg-Landau equation

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