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
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Bücher
Zeitschriften
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
ATZ-Fachkongress

Chassis.tech plus 2024


4 Kongresse in einer Veranstaltung

Treffen Sie in München die Fachleute von Chassis, Lenkung, Bremsen sowie Reifen/Räder.
Erweiterte Suche
Anmelden
nach oben
Engineering with Computers
Erschienen in: Engineering with Computers 2/2022

09.08.2020 | Original Article

A numerical solution of time-fractional mixed diffusion and diffusion-wave equation by an RBF-based meshless method

verfasst von: Akanksha Bhardwaj, Alpesh Kumar

Erschienen in: Engineering with Computers | Ausgabe 2/2022

Einloggen

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

search-config
loading …

Abstract

In this paper, we have developed an radial basis function (RBF) based meshless method to solve the time-fractional mixed diffusion and diffusion-wave equation which involves two fractional Caputo derivatives of order \(\alpha \in (0,1)\) and \(\beta \in (1,2)\). The unconditional stability of the proposed numerical scheme is discussed and proved theoretically. The time semi discretization has been done by using the finite difference method and for space discretization, we proposed an RBF-based local collocation method. Some test problems are considered for regular as well as an irregular domain with uniform and non-uniform points to validate the efficiency and accuracy of the method.
Vorheriger Artikel Two lopsided TSCSP (LTSCSP) iteration methods for solution of complex symmetric positive definite linear systems
Nächster Artikel A new multikernel relevance vector machine based on the HPSOGWO algorithm for predicting and controlling blast-induced ground vibration

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, Dehghan M (2017) An improved meshless method for solving two-dimensional distributed order time-fractional diffusion-wave equation with error estimate. Numer Algor 75(1):173–211MathSciNetMATH
2.
Abbaszadeh M, Dehghan M (2019) Meshless upwind local radial basis function-finite difference technique to simulate the time-fractional distributed-order advection–diffusion equation. In: Engineering with computers, pp 1–17
3.
Abbaszadeh M, Dehghan M (2020) A finite-difference procedure to solve weakly singular integro partial differential equation with space-time fractional derivatives. In: Engineering with computers, pp 1–10
4.
5.
6.
Aslefallah M, Shivanian E (2018) An efficient meshless method based on rbfs for the time fractional diffusion-wave equation. Afrika Matematika 29(7–8):1203–1214MathSciNetMATH
7.
Assari P, Cuomo S (2019) The numerical solution of fractional differential equations using the volterra integral equation method based on thin plate splines. Eng Comput 35(4):1391–1408
8.
Bagley RL, Torvik PJ (1983) A theoretical basis for the application of fractional calculus to viscoelasticity. J Rheol 27(3):201–210MATH
9.
Baseri A, Abbasbandy S, Babolian E (2018) A collocation method for fractional diffusion equation in a long time with chebyshev functions. Appl Math Comput 322:55–65MathSciNetMATH
10.
Bhardwaj A, Kumar A (2020) Numerical solution of time fractional tricomi-type equation by an rbf based meshless method. Eng Anal Bound Elem 118:96–107MathSciNetMATH
11.
Bhrawy AH, Zaky MA, Baleanu D (2015) New numerical approximations for space-time fractional burgers’ equations via a legendre spectral-collocation method. Rom Rep Phys 67(2):340–349
12.
Chen W, Ye L, Sun H (2010) Fractional diffusion equations by the kansa method. Comput Math Appl 59(5):1614–1620MathSciNetMATH
13.
Dehghan M, Abbaszadeh M (2018) An efficient technique based on finite difference/finite element method for solution of two-dimensional space/multi-time fractional bloch-torrey equations. Appl Numer Math 131:190–206MathSciNetMATH
14.
Dehghan M, Abbaszadeh M, Mohebbi A (2014) The numerical solution of nonlinear high dimensional generalized benjamin-bona-mahony-burgers equation via the meshless method of radial basis functions. Comput Math Appl 68(3):212–237MathSciNetMATH
15.
Dehghan M, Safarpoor M, Abbaszadeh M (2015) Two high-order numerical algorithms for solving the multi-term time fractional diffusion-wave equations. J Comput Appl Math 290:174–195MathSciNetMATH
16.
Dehghan M, Abbaszadeh M, Mohebbi A (2016) Analysis of a meshless method for the time fractional diffusion-wave equation. Numer Algor 73(2):445–476MathSciNetMATH
17.
Eshaghi J, Kazem S, Adibi H (2019) The local discontinuous galerkin method for 2d nonlinear time-fractional advection-diffusion equations. Eng Comput 35(4):1317–1332
18.
Fakhar-Izadi F (2020) Fully petrov–galerkin spectral method for the distributed-order time-fractional fourth-order partial differential equation. In: Engineering with computers, pp 1–10
19.
Feng L, Liu F, Turner I (2019) Finite difference/finite element method for a novel 2d multi-term time-fractional mixed sub-diffusion and diffusion-wave equation on convex domains. Commun Nonlinear Sci Numer Simul 70:354–371MathSciNetMATH
20.
Gao G, Sun Z, Zhang Y (2012) A finite difference scheme for fractional sub-diffusion equations on an unbounded domain using artificial boundary conditions. J Comput Phys 231(7):2865–2879MathSciNetMATH
21.
Ghehsareh HR, Zaghian A, Raei M (2018) A local weak form meshless method to simulate a variable order time-fractional mobile–immobile transport model. Eng Anal Bound Elem 90:63–75MathSciNetMATH
22.
Ghehsareh HR, Raei M, Zaghian A (2019) Application of meshless local petrov–galerkin technique to simulate two-dimensional time-fractional tricomi-type problem. J Braz Soc Mech Sci Eng 41(6):252
23.
Haq S, Hussain M, Ghafoor A (2019) A computational study of variable coefficients fractional advection–diffusion–reaction equations via implicit meshless spectral algorithm. In: Engineering with computers, pp 1–21
24.
Heydari MH, Avazzadeh Z (2020) New formulation of the orthonormal bernoulli polynomials for solving the variable-order time fractional coupled boussinesq–burger’s equations. In: Engineering with computers, pp 1–9
25.
Hidayat MIP, Ariwahjoedi B, Parman S (2016) B-spline collocation method for boundary value problems in complex domains. Int J Comput Sci Math 7(2):110–125MathSciNetMATH
26.
Hosseini VR, Shivanian E, Chen W (2016) Local radial point interpolation (mlrpi) method for solving time fractional diffusion-wave equation with damping. J Comput Phys 312:307–332MathSciNetMATH
27.
Hosseininia M, Heydari MH, Rouzegar J, Cattani C (2019) A meshless method to solve nonlinear variable-order time fractional 2d reaction–diffusion equation involving mittag-leffler kernel. In: Engineering with computers, pp 1–13
28.
Jin B, Lazarov R, Liu Y, Zhou Z (2015) The galerkin finite element method for a multi-term time-fractional diffusion equation. J Comput Phys 281:825–843MathSciNetMATH
29.
Karamali G, Dehghan M, Abbaszadeh M (2019) Numerical solution of a time-fractional pde in the electroanalytical chemistry by a local meshless method. Eng Comput 35(1):87–100
30.
Kazem S, Dehghan M (2019) Semi-analytical solution for time-fractional diffusion equation based on finite difference method of lines (mol). Eng Comput 35(1):229–241
31.
Kumar A, Bhardwaj A, Rathish Kumar BV (2019) A meshless local collocation method for time fractional diffusion wave equation. Comput Math Appl 78(6):1851–1861MathSciNetMATH
32.
Li X (2012) Numerical solution of fractional differential equations using cubic b-spline wavelet collocation method. Commun Nonlinear Sci Numer Simul 17(10):3934–3946MathSciNetMATH
33.
Li C, Wang Z (2019) The local discontinuous galerkin finite element methods for caputo-type partial differential equations: numerical analysis. Appl Numer Math 140:1–22MathSciNetMATH
34.
Liu Q, Gu YT, Zhuang P, Liu F, Nie YF (2011) An implicit rbf meshless approach for time fractional diffusion equations. Comput Mech 48(1):1–12MathSciNetMATH
35.
Liu Q, Liu F, Turner I, Anh V (2011) Finite element approximation for a modified anomalous subdiffusion equation. Appl Math Model 35(8):4103–4116MathSciNetMATH
36.
Liu Z, Liu F, Zeng F (2019) An alternating direction implicit spectral method for solving two dimensional multi-term time fractional mixed diffusion and diffusion-wave equations. Appl Numer Math 136:139–151MathSciNetMATH
37.
Liu Y, Sun HG, Yin X, Feng L (2020) Fully discrete spectral method for solving a novel multi-term time-fractional mixed diffusion and diffusion-wave equation. Zeitschrift für angewandte Mathematik und Physik 71(1):21MathSciNetMATH
38.
Lopez-Marcos JC (1990) A difference scheme for a nonlinear partial integrodifferential equation. SIAM J Numer Anal 27(1):20–31MathSciNetMATH
39.
Magin RL (2010) Fractional calculus models of complex dynamics in biological tissues. Comput Math Appl 59(5):1586–1593MathSciNetMATH
40.
Mardani A, Hooshmandasl MR, Heydari MH, Cattani C (2018) A meshless method for solving the time fractional advection–diffusion equation with variable coefficients. Comput Math Appl 75(1):122–133MathSciNetMATH
41.
Metzler R, Klafter J (2004) The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics. J Phys A Math Gen 37(31):R161MathSciNetMATH
42.
Mirzaee F, Samadyar N (2019) Combination of finite difference method and meshless method based on radial basis functions to solve fractional stochastic advection–diffusion equations. In: Engineering with computers, pp 1–14
43.
Mohebbi A, Abbaszadeh M, Dehghan M (2014) The meshless method of radial basis functions for the numerical solution of time fractional telegraph equation. Int J Numer Methods Heat Fluid Flow
44.
Nagy AM (2017) Numerical solution of time fractional nonlinear klein-gordon equation using sinc-chebyshev collocation method. Appl Math Comput 310:139–148MathSciNetMATH
45.
Oruç Ö (2019) A meshless multiple-scale polynomial method for numerical solution of 3d convection–diffusion problems with variable coefficients. Eng Comput x:1–14
46.
Oruç Ö, Esen A, Bulut F (2019) A haar wavelet approximation for two-dimensional time fractional reaction-subdiffusion equation. Eng Comput 35(1):75–86
47.
Safari F, Azarsa P (2019) Backward substitution method based on müntz polynomials for solving the nonlinear space fractional partial differential equations. Math Methods Appl Sci
48.
Salehi R (2017) A meshless point collocation method for 2-d multi-term time fractional diffusion-wave equation. Numer Algor 74(4):1145–1168MathSciNetMATH
49.
Shivanian E, Jafarabadi A (2018) The spectral meshless radial point interpolation method for solving an inverse source problem of the time-fractional diffusion equation. Appl Numer Math 129:1–25MathSciNetMATH
50.
Sun Z, Xiaonan W (2006) A fully discrete difference scheme for a diffusion-wave system. Appl Numer Math 56(2):193–209MathSciNetMATH
51.
Sun Z, Ji C, Ruilian D (2020) A new analytical technique of the l-type difference schemes for time fractional mixed sub-diffusion and diffusion-wave equations. Appl Math Lett 102:106115MathSciNetMATH
52.
Tayebi A, Shekari Y, Heydari MH (2017) A meshless method for solving two-dimensional variable-order time fractional advection–diffusion equation. J Comput Phys 340:655–669MathSciNetMATH
53.
Vong S, Wang Z (2014) A compact difference scheme for a two dimensional fractional klein-gordon equation with neumann boundary conditions. J Comput Phys 274:268–282MathSciNetMATH
54.
Wei S, Chen W, Hon Y-C (2015) Implicit local radial basis function method for solving two-dimensional time fractional diffusion equations. Therm Sci 19(suppl. 1):59–67
55.
Yang JY, Zhao YM, Liu N, Bu WP, Xu TL, Tang YF (2015) An implicit mls meshless method for 2-d time dependent fractional diffusion-wave equation. Appl Math Model 39(3–4):1229–1240MathSciNetMATH
56.
Yuste SB, Acedo L (2005) An explicit finite difference method and a new von neumann-type stability analysis for fractional diffusion equations. SIAM J Numer Anal 42(5):1862–1874MathSciNetMATH
57.
Zeng F, Zhang Z, Karniadakis GE (2016) Fast difference schemes for solving high-dimensional time-fractional subdiffusion equations. J Comput Phys 307:15–33MathSciNetMATH
58.
Zhao Y, Wang F, Xiaohan H, Shi Z, Tang Y (2019) Anisotropic linear triangle finite element approximation for multi-term time-fractional mixed diffusion and diffusion-wave equations with variable coefficient on 2d bounded domain. Comput Math Appl 78(5):1705–1719MathSciNetMATH
59.
Zhuang P, Gu YT, Liu F, Turner I, Yarlagadda PKDV (2011) Time-dependent fractional advection–diffusion equations by an implicit mls meshless method. Int J Numer Meth Eng 88(13):1346–1362MathSciNetMATH
Metadaten
Titel
A numerical solution of time-fractional mixed diffusion and diffusion-wave equation by an RBF-based meshless method
verfasst von
Akanksha Bhardwaj
Alpesh Kumar
Publikationsdatum
09.08.2020
Verlag
Springer London
Erschienen in
Engineering with Computers / Ausgabe 2/2022
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-020-01134-4

Weitere Artikel der Ausgabe 2/2022

Engineering with Computers 2/2022 Zur Ausgabe

Original Article

A new formulation for non-equilibrium capillarity effect using multi-gene genetic programming (MGGP): accounting for fluid and porous media properties

Original Article

Selection scheme sensitivity for a hybrid Salp Swarm Algorithm: analysis and applications

Original Article

Symbolic regression metamodel-based optimal design of patient-specific spinal implant (pedicle screw fixation)

Original Article

Chaotic oppositional sine–cosine method for solving global optimization problems

Original Article

A new variable-order fractional derivative with non-singular Mittag–Leffler kernel: application to variable-order fractional version of the 2D Richard equation

Original Article

An efficient and accurate hybrid weak-form meshless method for transient nonlinear heterogeneous heat conduction problems

Neuer Inhalt

    Bildnachweise