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 3/2017

05.04.2017 | Original Article

Application of quintic B-splines collocation method for solving inverse Rosenau equation with Dirichlet’s boundary conditions

verfasst von: Akram Saeedi, Reza Pourgholi

Erschienen in: Engineering with Computers | Ausgabe 3/2017

Einloggen

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

search-config
loading …

Abstract

In this paper, we discuss a numerical method for solving an inverse Rosenau equation with Dirichlet’s boundary conditions. The approach used is based on collocation of a quintic B-spline over finite elements so that we have continuity of dependent variable and it first four derivatives throughout the solution range. We apply quintic B-spline for spatial variable and derivatives which produce an ill-posed system. We solve this system using Tikhonov regularization method. The accuracy of the proposed method is demonstrated by applying it on a test problem. Figures and comparisons have been presented for clarity. The main advantage of the resulting scheme is that the algorithm is very simple, so it is very easy to implement.
Nächster Artikel Developing a new hybrid-AI model to predict blast-induced backbreak

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.
Aguero M, Ongay F, Sanchez-Mondragon J (2011) Nonclassical solitary waves for nonlinear ordinary differential equation. Fundam J Mod Phys 1:41–62
2.
Biswas A (2010) 1-Soliton solution of the \(K(m, n)\) equation with generalized evolution and time-dependent damping and dispersion. Comput Math Appl 59:2538–2542MathSciNetCrossRef
3.
Biswas A, Triki H, Labidi M (2011) Bright and dark solitons of the Rosenau–Kawahara equation with power law nonlinearity. Phys Wave Phenom 19:24–29CrossRef
4.
Ebadi G, Biswas A (2011) The \(\frac{G^{\prime }}{G}\) method and topological soliton solution of the \(K(m, n)\) equation. Commun Nonlinear Sci Numer Simul 16:2377–2382MathSciNetCrossRefMATH
5.
Inc M, Ulutas E, Cavlak E, Biswas A (2013) Singular 1-soliton solution of the \(K(m, n)\) equation with generalized evolutions and its subsidiaries. Acta Phys Polon B 44:1825–1836MathSciNetCrossRef
6.
Antonova M, Biswas A (2009) Adiabatic parameter dynamics of perturbed solitary waves. Commun Nonlinear Sci Numer Simul 14:734–748MathSciNetCrossRefMATH
7.
Biswas A (2009) solitary wave solution for the generalized kdv equation with time-dependent damping and dispersion. Commun Nonlinear Sci Numer Simul 14:3503–3506MathSciNetCrossRefMATH
8.
Ebadi G, Mojaver A, Triki H, Yildirim A, Biswas A (2013) Topological solitons and other solutions of the Rosenau-KdV equation with power law nonlinearity. Rom J Phys 58:3–14MathSciNet
9.
Razborova P, Ahmed B, Biswas A (2014) Solitons, shock waves and conservation laws of Rosenau-KdV-RLW equation with power law nonlinearity. Appl Math Inf Sci 8:485–491MathSciNetCrossRef
10.
Razborova P, Triki H, Biswas A (2013) Perturbation of dispersive shallow water waves. Ocean Eng 63:1–7CrossRef
11.
12.
Rosenau P (1986) A quasi-continuous description of a nonlinear transmission line. Phys Script 349:827–829CrossRef
13.
Rosenau P (1988) Dynamics of the dense discrete systems. Prog Theor Phys 79:1028–1042CrossRef
14.
15.
16.
17.
Mittal RC, Jain RK (2012) Numerical solution of general Rosenau-RLW equation using Quintic B-splines collocation method, volume 2012, p 16, Article ID cna-00129
18.
Abtahi M, Pourgholi R, Shidfar A (2011) Existence and uniqueness of solution for a two dimensional nonlinear inverse diffusion problem. Nonlinear Anal 74:2462–2467MathSciNetCrossRefMATH
19.
Pourgholi R, Dana H, Tabasi SH (2014) Solving an inverse heat conduction problem using genetic algorithm: sequential and multi-core parallelization approach. Appl Math Model 38:1948–1958MathSciNetCrossRef
20.
Pourgholi R, Esfahani A (2013) An efficient numerical method for solving an inverse wave problem. IJCM. 10
21.
Pourgholi R, Esfahani A, Rahimi H, Tabasi SH (2013) Solving an inverse initial-boundary-value problem by using basis function method. Comput Appl Math 1:27–32CrossRefMATH
22.
Pourgholi R, Rostamian M, Emamjome M (2010) A numerical method for solving a nonlinear inverse parabolic problem. Inverse Probl Sci Eng 8:1151–1164MathSciNetCrossRefMATH
23.
24.
Pourgholi R, Tavallaie N, Foadian S (2012) Applications of Haar basis method for solving some ill-posed inverse problems. J Math Chem 8:2317–2337MathSciNetCrossRefMATH
25.
Tikhonov AN, Arsenin VY (1977) Solution of Ill-posed problems. V. H. Winston and Sons, Washington, DCMATH
26.
27.
Murio DA (1993) The mollification method and the numerical solution of Ill-posed problems. Wiley, NewYorkCrossRef
28.
Pourgholi R, Rostamian M (2010) A numerical technique for solving IHCPs using Tikhonov regularization method. Appl Math Model 34:2102–2110MathSciNetCrossRefMATH
29.
Molhem H, Pourgholi R (2008) A numerical algorithm for solving a one-dimensional inverse heat conduction problem. J Math Stat 4:60–63MathSciNetCrossRefMATH
30.
Beck JV, Blackwell B, St CR (1985) Clair, inverse heat conduction: Ill posed problems. Wiley, NewYork
31.
Zhou J, Zhang Y, Chen JK, Feng ZC (2010) Inverse heat conduction in a composite slab with pyrolysis effect and temperature-dependent thermophysical properties. J Heat Transf 132(3):034502CrossRef
32.
Huanga C-H, Yeha C-Y, Orlande HRB (2003) A nonlinear inverse problem in simultaneously estimating the heat and mass production rates for a chemically reacting fluid. Chem Eng Sci 58(16):3741–3752CrossRef
33.
Caglar H, Caglar N, Elfaituri K (2006) B-spline interpolation compared with finite element and finite volume methods which applied to two point boundary value problems. Appl Math Comput 175:72–79MathSciNetMATH
34.
Caglar N, Caglar H (2006) B-spline solution of singular boundary value problems. Appl Math Comput 182:1509–1513MathSciNetMATH
35.
Caglar H, Ozer M, Caglar N (2008) The numerical solution of the one dimensional heat equation by using third degree B-spline functions. Chaos Solitons Fract 38:1197–1201CrossRefMATH
36.
Mittal RC, Jain RK (2012) Application of quintic B-splines collocation method on some Rosenau type nonlinear higher order evolution equations. Int J Nonlinear Sci 13:142–152MathSciNetMATH
37.
Mittal RC, Arora G (2011) Numerical solution of the coupled viscous Burger’s equation. Commun Nonlinear Sci Numer Simul 16:1304–1313MathSciNetCrossRefMATH
38.
39.
40.
Tikhonov AN, Arsenin VY (1977) On the solution of ill-posed problems. Wiley, New YorkMATH
41.
Martin L, Elliott L, Heggs PJ, Ingham DB, Lesnic D, Wen X (2006) Dual reciprocity boundary element method solution of the Cauchy problem for Helmholtz-type equations with variable coefficients. J Sound Vibr 297:89–105CrossRefMATH
42.
Elden L (1984) A note on the computation of the generalized cross-validation function for Ill-conditioned least squares problems. BIT 24:467–472MathSciNetCrossRefMATH
43.
Golub GH, Heath M, Wahba G (1979) Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21(2):215–223MathSciNetCrossRefMATH
44.
45.
46.
Rudin W (1976) Principles of mathematical analysis, 3rd edn. McGraw-Hill Inc., PennsylvaniaMATH
47.
Kadalbajoo MK, Gupta V, Awasthi A (2008) A uniformly convergent B-spline collocation method on a nonuniform mesh for singularly perturbed one-dimensional time-dependent linear convection diffusion problem. J Comput Appl Math 220:271–289MathSciNetCrossRefMATH
48.
Smith GD (1978) Numerical solution of partial differential equation: finite difference method. Learendom Press, Oxford
49.
Mittal RC, Jain RK (2012) Application of quintic B-spline collocation method on some Rosenau type nonlinear higher order evolution equations. J Inf Comput Sci 7(2):083–090MathSciNetMATH
50.
Gottlieb S, Shu C-W, Tadmor E (2001) Strong stability-preserving high-order time discretization methods. SIAM REV 43(1):89–112MathSciNetCrossRefMATH
51.
Guraslan G, Sari M (2011) Numerical solutions of liner and nonlinear diffusion equations by a differential quadrature method (DQM). Int J Numer Methods Biomed Eng 27:69–77CrossRef
52.
Huang CH, Tsai YL (2005) A transient 3-D inverse problem in imaging the time dependentlocal heat transfer coefficients for plate fin. Appl Therm Eng 25:2478–2495CrossRef
53.
Mittal RC, Jain RK (2012) Cubic B-spline collocation method for solving nonlinear parabolic partial differential equations with Neumann boundary conditions. Commun Nonlinear Sci Numer Simul 17:4616–4625MathSciNetCrossRefMATH
54.
Rashidinia J, Ghasemi M, Jalilian R (2010) A collocation method for the solution of nonlinear one dimensional parabolic equations. Math Sci 4(1):87–104MathSciNetMATH
55.
Metadaten
Titel
Application of quintic B-splines collocation method for solving inverse Rosenau equation with Dirichlet’s boundary conditions
verfasst von
Akram Saeedi
Reza Pourgholi
Publikationsdatum
05.04.2017
Verlag
Springer London
Erschienen in
Engineering with Computers / Ausgabe 3/2017
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-017-0512-3

Weitere Artikel der Ausgabe 3/2017

Engineering with Computers 3/2017 Zur Ausgabe

Original Article

A virus-evolutionary multi-objective intelligent tool path optimization methodology for 5-axis sculptured surface CNC machining

Original Article

Global optimization method using ensemble of metamodels based on fuzzy clustering for design space reduction

Original Article

Zoned elasticity modulus inversion analysis method of a high arch dam based on unconstrained Lagrange support vector regression (support vector regression arch dam)

Original Article

Evaluating the modulus of elasticity of soil using soft computing system

Original Article

Application of JAYA algorithm for the optimization of machining performance characteristics during the turning of CFRP (epoxy) composites: comparison with TLBO, GA, and ICA

Original Article

An automated computationally efficient two-stage procedure for service load analysis of RC flexural members considering concrete cracking

Neuer Inhalt

    Bildnachweise