Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Engineering with Computers
Erschienen in: Engineering with Computers 2/2021

01.10.2019 | Original Article

Meshless upwind local radial basis function-finite difference technique to simulate the time- fractional distributed-order advection–diffusion equation

verfasst von: Mostafa Abbaszadeh, Mehdi Dehghan

Erschienen in: Engineering with Computers | Ausgabe 2/2021

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The main objective in this paper is to propose an efficient numerical formulation for solving the time-fractional distributed-order advection–diffusion equation. First, the distributed-order term has been approximated by the Gauss quadrature rule. In the next, a finite difference approach is applied to approximate the temporal variable with convergence order \(\mathcal{O}(\tau ^{2-\alpha })\) as \(0<\alpha <1\). Finally, to discrete the spacial dimension, an upwind local radial basis function-finite difference idea has been employed. In the numerical investigation, the effect of the advection coefficient has been studied in terms of accuracy and stability of the proposed difference scheme. At the end, two examples are studied to approve the impact and ability of the numerical procedure.
Vorheriger Artikel The parameterized level set method for structural topology optimization with shape sensitivity constraint factor
Nächster Artikel Strength evaluation of granite block samples with different predictive models

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Literatur
1.
Abbaszadeh M (2019) Error estimate of second-order finite difference scheme for solving the Riesz space distributed-order diffusion equation. Appl Math Lett 88:179–185MathSciNetMATH
2.
Abbaszadeh M, Dehghan M (2017) An improved meshless method for solving two-dimensional distributed order time-fractional diffusion-wave equation with error estimate. Numer Algorithms 75:173–211MathSciNetMATH
3.
Aliyu AI, Inc M, Yusuf A, Baleanu D (2018) A fractional model of vertical transmission and cure of vector-borne diseases pertaining to the Atangana–Baleanu fractional derivatives. Chaos Solitons Fractals 116:268–277MathSciNetMATH
4.
Atanackovic T, Pilipovic S, Zorica D (2009) Existence and calculation of the solution to the time distributed order diffusion equation. Phys Scr 2009(T136):014012
5.
Atanackovic TM, Pilipovic S, Zorica D (2009) Time distributed-order diffusion–wave equation. i. Volterra-type equation. In: Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, The Royal Society, pp rspa–2008
6.
Atangana A, Koca I (2016) Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order. Chaos Solitons Fractals 89:447–454MathSciNetMATH
7.
Atangana A, Gomez-Aguilar JF (2018) Fractional derivatives with no-index law property: application to chaos and statistics. Chaos Solitons Fractals 114:516–535MathSciNetMATH
8.
Atkinson KE An introduction to numerical analysis, New York, p 528
9.
Bhrawy AH, Zaky MA (2018) Numerical simulation of multi-dimensional distributed-order generalized Schrodinger equations. Nonlinear Dyn 89:1415–1432MATH
10.
Chechkin A, Gorenflo R, Sokolov I (2002) Retarding subdiffusion and accelerating superdiffusion governed by distributed-order fractional diffusion equations. Phys Rev E 66(4):046129
11.
Chechkin AV, Gorenflo R, Sokolov IM, Gonchar VY (2003) Distributed order time fractional diffusion equation. Fract Calc Appl Anal 6(3):259–280MathSciNetMATH
12.
Dehghan M (2004) Weighted finite difference techniques for the one-dimensional advection–diffusion equation. Appl Math Comput 147(2):307–319MathSciNetMATH
13.
Dehghan M, Abbaszadeh M (2018) A Legendre spectral element method (SEM) based on the modified bases for solving neutral delay distributed-order fractional damped diffusion-wave equation. Math Methods Appl Sci 41:3476–3494MathSciNetMATH
14.
Dehghan M, Abbaszadeh M (2017) A finite element method for the numerical solution of Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivatives. Eng Comput 33:587–605
15.
Dehghan M, Abbaszadeh M (2019) Error estimate of finite element/finite difference technique for solution of two-dimensional weakly singular integro-partial differential equation with space and time fractional derivatives. J Comput Appl Math 356:314–328MathSciNetMATH
16.
Dehghan M, Manafian J, Saadatmandi A (2010) Solving nonlinear fractional partial differential equations using the homotopy analysis method. Numer Methods Partial Differ Equ 26:448–479MathSciNetMATH
17.
Ding H, Li CP (2019) A high-order algorithm for time-caputo-tempered partial differential equation with Riesz derivatives in two spatial dimensions. J Sci Comput 80:81–109MathSciNetMATH
18.
Ding H (2019) A high-order numerical algorithm for two-dimensional time-space tempered fractional diffusion-wave equation. Appl Numer Math 135:30–46MathSciNetMATH
19.
Ding H, Li CP (2018) High-order numerical approximation formulas for Riemann–Liouville (Riesz) tempered fractional derivatives: construction and application (II). Appl Math Lett 86:208–214MathSciNetMATH
20.
Ding H, Li CP (2017) High-order numerical algorithms for Riesz derivatives via constructing new generating functions. J Sci Comput 71(2):759–784MathSciNetMATH
21.
Driscoll TA, Fornberg B (2002) Interpolation in the limit of increasingly flat radial basis functions. Comput Math Appl 43(3–5):413–422MathSciNetMATH
22.
23.
Flyer N, Lehto E, Blaise S, Wright GB, St-Cyr A (2012) A guide to RBF-generated finite differences for nonlinear transport: shallow water simulations on a sphere. J Comput Phys 231(11):4078–4095MathSciNetMATH
24.
Fornberg B, Lehto E (2011) Stabilization of RBF-generated finite difference methods for convective PDEs. J Comput Phys 230(6):2270–2285MathSciNetMATH
25.
Gao G-H, Sun Z-Z (2015) Two alternating direction implicit difference schemes with the extrapolation method for the two-dimensional distributed-order differential equations. Comput Math Appl 69(9):926–948MathSciNetMATH
26.
Javed A, Djijdeli K, Xing J (2014) Shape adaptive RBF-FD implicit scheme for incompressible viscous Navier–Stokes equations. Comput Fluids 89:38–52MathSciNetMATH
27.
28.
Katsikadelis JT (2014) Numerical solution of distributed order fractional differential equations. J Comput Phys 259:11–22MathSciNetMATH
29.
Li C, Deng W, Zhao L (2019) Well-posedness and numerical algorithm for the tempered fractional differential equations. Discret Contin Dyn Syst B 24:1989MathSciNetMATH
30.
Luchko Y (2009) Boundary value problems for the generalized time-fractional diffusion equation of distributed order. Fract Calc Appl Anal 12(4):409–422MathSciNetMATH
31.
Hu X, Liu F, Turner I, Anh V (2016) An implicit numerical method of a new time distributed-order and two-sided space-fractional advection–dispersion equation. Numer Algorithms 72:393–407MathSciNetMATH
32.
Mashayekhi S, Razzaghi M (2016) Numerical solution of distributed order fractional differential equations by hybrid functions. J Comput Phys 315:169–181MathSciNetMATH
33.
Moghaddam BP, Machado JAT, Morgado ML (2019) Numerical approach for a class of distributed order time fractional partial differential equations. Appl Numer Math 136:152–162MathSciNetMATH
34.
Osman SA, Langlands TAM (2019) An implicit Keller Box numerical scheme for the solution of fractional subdiffusion equations. Appl Math Comput 348:609–626MathSciNetMATH
35.
Podlubny I, Skovranek T, Jara BMV, Petras I, Verbitsky V, Chen Y (2013) Matrix approach to discrete fractional calculus iii: non-equidistant grids, variable step length and distributed orders. Philos Trans R Soc A 371(1990):20120153MathSciNetMATH
36.
Qiao Y, Zhai S, Feng X (2017) RBF-FD method for the high dimensional time fractional convection–diffusion equation. Int Commun Heat Mass Transfer 89:230–240
37.
Sandev T, Chechkin AV, Korabel N, Kantz H, Sokolov IM, Metzler R (2015) Distributed-order diffusion equations and multifractality: models and solutions. Phys Rev E 92(4):042117MathSciNet
38.
Shankar V (2017) The overlapped radial basis function-finite difference (RBF-FD) method: a generalization of RBF-FD. J Comput Phys 342:211–228MathSciNetMATH
39.
Shu C, Ding H, Chen H, Wang T (2005) An upwind local RBF-DQ method for simulation of inviscid compressible flows. Comput Methods Appl Mech Eng 194(18–20):2001–2017MATH
40.
Sun Z-Z, Wu X (2006) A fully discrete difference scheme for a diffusion-wave system. Appl Numer Math 56(2):193–209MathSciNetMATH
41.
Wang X, Deng W Discontinuous Galerkin methods and their adaptivity for the tempered fractional (convection) diffusion equations. arXiv:​1706.​02826 (arXiv preprint)
42.
Wendland H (2004) Scattered data approximation, vol 17. Cambridge University Press, CambridgeMATH
43.
Ye H, Liu F, Anh V (2015) Compact difference scheme for distributed-order time-fractional diffusion-wave equation on bounded domains. J Comput Phys 298:652–660MathSciNetMATH
44.
Yuttanana B, Razzaghi M (2019) Legendre wavelets approach for numerical solutions of distributed order fractional differential equations. Appl Math Model 70:350–364MathSciNetMATH
45.
Zaky MA (2018) An improved tau method for the multi-dimensional fractional Rayleigh–Stokes problem for a heated generalized second grade fluid. Comput Math Appl 75:2243–2258MathSciNetMATH
46.
Zaky MA, Machado JAT (2017) On the formulation and numerical simulation of distributed-order fractional optimal control problems. Commun Nonlinear Sci Numer Simul 52:177–189MathSciNetMATH
47.
Zaky MA, Doha EH, Machado JAT (2018) A spectral numerical method for solving distributed-order fractional initial value problems. J Comput Nonlinear Dyn 3(10):101007
48.
Zaky MA (2018) A Legendre collocation method for distributed-order fractional optimal control problems. Nonlinear Dyn 91:2667–2681MATH
49.
50.
Zaky MA (2019) Recovery of high order accuracy in Jacobi spectral collocation methods for fractional terminal value problems with non-smooth solutions. J Comput Appl Math 357:103–122MathSciNetMATH
51.
52.
Zayernouri M, Karniadakis GE (2014) Discontinuous spectral element methods for time-and space-fractional advection equations. SIAM J Sci Comput 36(4):B684–B707MathSciNetMATH
53.
Zhao X, Sun Z-Z, Karniadakis GE (2015) Second-order approximations for variable order fractional derivatives: algorithms and applications. J Comput Phys 293:184–200MathSciNetMATH
Metadaten
Titel
Meshless upwind local radial basis function-finite difference technique to simulate the time- fractional distributed-order advection–diffusion equation
verfasst von
Mostafa Abbaszadeh
Mehdi Dehghan
Publikationsdatum
01.10.2019
Verlag
Springer London
Erschienen in
Engineering with Computers / Ausgabe 2/2021
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-019-00861-7

Weitere Artikel der Ausgabe 2/2021

Engineering with Computers 2/2021 Zur Ausgabe

Original Article

Local radial basis function–finite-difference method to simulate some models in the nonlinear wave phenomena: regularized long-wave and extended Fisher–Kolmogorov equations

Original Article

Applying a meta-heuristic algorithm to predict and optimize compressive strength of concrete samples

Original Article

Legendre multiwavelet functions for numerical solution of multi-term time-space convection–diffusion equations of fractional order

Original Article

Predictive modeling of the lateral drift capacity of circular reinforced concrete columns using an evolutionary algorithm

Original Article

A success history-based adaptive differential evolution optimized support vector regression for estimating plastic viscosity of fresh concrete

Original Article

Vibration analysis of porous magneto-electro-elastically actuated carbon nanotube-reinforced composite sandwich plate based on a refined plate theory

Neuer Inhalt

    Bildnachweise