메뉴 건너뛰기




Volumn 36, Issue 1, 2012, Pages 158-167

Differential quadrature method (DQM) and Boubaker Polynomials Expansion Scheme (BPES) for efficient computation of the eigenvalues of fourth-order Sturm-Liouville problems

Author keywords

Boubaker Polynomials Expansion Scheme (BPES); Boundary value problems; Differential quadrature method (DQM); Eigenvalue problems; Sturm Liouville problems

Indexed keywords

BOUNDARY POINTS; COMPUTATIONAL DOMAINS; DIFFERENTIAL QUADRATURE METHOD (DQM); DIFFERENTIAL QUADRATURE METHODS; EFFICIENT COMPUTATION; EIGENVALUE PROBLEM; EIGENVALUES; EULER-BERNOULLI BEAM EQUATION; FOURTH-ORDER; GOVERNING EQUATIONS; MESH POINTS; NUMERICAL EXAMPLE; POLYNOMIALS EXPANSION; STURM-LIOUVILLE PROBLEM;

EID: 80051825972     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2011.05.030     Document Type: Article
Times cited : (30)

References (39)
  • 2
    • 0024740363 scopus 로고
    • One-dimensional heat and mass diffusion modeling
    • Barouh V.A., Mikhailov M.D. One-dimensional heat and mass diffusion modeling. Appl. Math. Model. 1989, 13:568-573.
    • (1989) Appl. Math. Model. , vol.13 , pp. 568-573
    • Barouh, V.A.1    Mikhailov, M.D.2
  • 3
    • 77954031276 scopus 로고    scopus 로고
    • 3D free vibration analysis of laminated cylindrical shell integrated piezoelectric layers using the differential quadrature method
    • Alibeigloo A., Kani A.M. 3D free vibration analysis of laminated cylindrical shell integrated piezoelectric layers using the differential quadrature method. Appl. Math. Model. 2010, 34:4123-4137.
    • (2010) Appl. Math. Model. , vol.34 , pp. 4123-4137
    • Alibeigloo, A.1    Kani, A.M.2
  • 4
    • 69249222804 scopus 로고    scopus 로고
    • A coupled finite element-differential quadrature element method and its accuracy for moving load problem
    • Eftekhari S.A., Khani M. A coupled finite element-differential quadrature element method and its accuracy for moving load problem. Appl. Math. Model. 2010, 34:228-237.
    • (2010) Appl. Math. Model. , vol.34 , pp. 228-237
    • Eftekhari, S.A.1    Khani, M.2
  • 5
    • 68049142267 scopus 로고    scopus 로고
    • A semi-analytic approach for the nonlinear dynamic response of circular plates
    • Peng J.S., Yuan Y.Q., Yang J., Kitipornchai S. A semi-analytic approach for the nonlinear dynamic response of circular plates. Appl. Math. Model. 2009, 33:4303-4313.
    • (2009) Appl. Math. Model. , vol.33 , pp. 4303-4313
    • Peng, J.S.1    Yuan, Y.Q.2    Yang, J.3    Kitipornchai, S.4
  • 6
    • 33646081035 scopus 로고    scopus 로고
    • Approximations of Sturm-Liouville eigenvalues using differential quadrature (DQ) method
    • Yücel U. Approximations of Sturm-Liouville eigenvalues using differential quadrature (DQ) method. J. Comput. Appl. Math. 2006, 192:310-319.
    • (2006) J. Comput. Appl. Math. , vol.192 , pp. 310-319
    • Yücel, U.1
  • 8
    • 0038659316 scopus 로고
    • An oscillation method for fourth order self-adjoint two-point boundary value problems with nonlinear eigenvalues
    • Greenberg L. An oscillation method for fourth order self-adjoint two-point boundary value problems with nonlinear eigenvalues. SIAM J. Math. Anal. 1991, 22:1021-1042.
    • (1991) SIAM J. Math. Anal. , vol.22 , pp. 1021-1042
    • Greenberg, L.1
  • 9
    • 0038931055 scopus 로고
    • Oscillation theory and numerical solution of fourth order Sturm-Liouville problems
    • Greenberg L., Marletta M. Oscillation theory and numerical solution of fourth order Sturm-Liouville problems. IMA J. Numer. Anal. 1995, 15:319-356.
    • (1995) IMA J. Numer. Anal. , vol.15 , pp. 319-356
    • Greenberg, L.1    Marletta, M.2
  • 10
    • 0031376840 scopus 로고    scopus 로고
    • Algorithm 775: the code SLEUTH for solving fourth order Sturm-Liouville problems
    • Greenberg L., Marletta M. Algorithm 775: the code SLEUTH for solving fourth order Sturm-Liouville problems. ACM Trans. Math. Software 1997, 23:453-493.
    • (1997) ACM Trans. Math. Software , vol.23 , pp. 453-493
    • Greenberg, L.1    Marletta, M.2
  • 12
    • 80051804450 scopus 로고
    • Computing Eigenvalues of Singular Sturm-Liouville Problems, Results in Mathematics, Birkhauser, Basel
    • P.B. Bailey, W.N. Everitt, A. Zeal, Computing Eigenvalues of Singular Sturm-Liouville Problems, Results in Mathematics, vol. 20, Birkhauser, Basel, 199l.
    • (1991) , vol.20
    • Bailey, P.B.1    Everitt, W.N.2    Zeal, A.3
  • 13
    • 80051809317 scopus 로고
    • Mathematical Software for Sturm-Liouville Problems, NSF Final Report for Grants DMS88-13113 and DMS88-00839, Computational Mathematics Division
    • C. Fulton, S. Pruess, Mathematical Software for Sturm-Liouville Problems, NSF Final Report for Grants DMS88-13113 and DMS88-00839, Computational Mathematics Division, 1991.
    • (1991)
    • Fulton, C.1    Pruess, S.2
  • 14
    • 0040962526 scopus 로고    scopus 로고
    • Eigenvalues of fourth order Sturm-Liouville problems using Fliess series
    • Chanane B. Eigenvalues of fourth order Sturm-Liouville problems using Fliess series. J. Comput. Appl. Math. 1998, 96:91-97.
    • (1998) J. Comput. Appl. Math. , vol.96 , pp. 91-97
    • Chanane, B.1
  • 15
    • 31244435373 scopus 로고    scopus 로고
    • Fliess series approach to the computation of the eigenvalues of fourth order Sturm-Liouville problems
    • Chanane B. Fliess series approach to the computation of the eigenvalues of fourth order Sturm-Liouville problems. Appl. Math. Lett. 2002, 15:459-463.
    • (2002) Appl. Math. Lett. , vol.15 , pp. 459-463
    • Chanane, B.1
  • 16
    • 33751512653 scopus 로고    scopus 로고
    • An efficient method for computing eigenelements of Sturm-Liouville fourth-order boundary value problems
    • Attili B.S., Lesnic D. An efficient method for computing eigenelements of Sturm-Liouville fourth-order boundary value problems. Appl. Math. Comput. 2006, 182:1247-1254.
    • (2006) Appl. Math. Comput. , vol.182 , pp. 1247-1254
    • Attili, B.S.1    Lesnic, D.2
  • 17
    • 62549132486 scopus 로고    scopus 로고
    • An efficient technique for finding the eigenvalues of fourth-order Sturm-Liouville problems
    • Syam M.I., Siyyam H.I. An efficient technique for finding the eigenvalues of fourth-order Sturm-Liouville problems. Chaos Solitons Fract. 2009, 39:659-665.
    • (2009) Chaos Solitons Fract. , vol.39 , pp. 659-665
    • Syam, M.I.1    Siyyam, H.I.2
  • 18
    • 77955275577 scopus 로고    scopus 로고
    • Accurate solutions of fourth order Sturm-Liouville problems
    • Chanane B. Accurate solutions of fourth order Sturm-Liouville problems. J. Comput. Appl. Math. 2010, 234:3064-3071.
    • (2010) J. Comput. Appl. Math. , vol.234 , pp. 3064-3071
    • Chanane, B.1
  • 19
    • 37249061595 scopus 로고    scopus 로고
    • Sturm-Liouville problems with parameter dependent potential and boundary conditions
    • Chanane B. Sturm-Liouville problems with parameter dependent potential and boundary conditions. J. Comput. Appl. Math. 2008, 212:282-290.
    • (2008) J. Comput. Appl. Math. , vol.212 , pp. 282-290
    • Chanane, B.1
  • 20
    • 77955927814 scopus 로고    scopus 로고
    • A new application of the homotopy analysis method: solving the Sturm-Liouville problems, Commun. Nonlinear Sci. Numer. Simulat.
    • S. Abbasbandy, A. Shirzadi, A new application of the homotopy analysis method: solving the Sturm-Liouville problems, Commun. Nonlinear Sci. Numer. Simulat. doi:10.1016/j.cnsns.2010.04.004.
    • Abbasbandy, S.1    Shirzadi, A.2
  • 21
    • 0002800312 scopus 로고
    • Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations
    • Bellman R., Kashef B.G., Casti J. Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations. J. Comput. Phys. 1972, 10:40-52.
    • (1972) J. Comput. Phys. , vol.10 , pp. 40-52
    • Bellman, R.1    Kashef, B.G.2    Casti, J.3
  • 22
    • 80051803916 scopus 로고
    • Generalized Differential-integral Quadrature and Application to the Simulation of Incompressible Viscous Flows Including Parallel Computation, Ph.D. Thesis, University of Glasgow, UK
    • C. Shu, Generalized Differential-integral Quadrature and Application to the Simulation of Incompressible Viscous Flows Including Parallel Computation, Ph.D. Thesis, University of Glasgow, UK, 1991.
    • (1991)
    • Shu, C.1
  • 23
    • 0026939625 scopus 로고
    • Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations
    • Shu C., Richards B.E. Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations. Int. J. Numer. Methods Fluids 1992, 15:791-798.
    • (1992) Int. J. Numer. Methods Fluids , vol.15 , pp. 791-798
    • Shu, C.1    Richards, B.E.2
  • 24
    • 0030237098 scopus 로고    scopus 로고
    • Numerical studies of unsteady boundary layer flows past an impulsively started circular cylinder by GDQ and GIQ approaches
    • Shu C., Khoo B.C., Chew Y.T., Yeo K.S. Numerical studies of unsteady boundary layer flows past an impulsively started circular cylinder by GDQ and GIQ approaches. Comput. Methods Appl. Mech. Eng. 1996, 135:229-241.
    • (1996) Comput. Methods Appl. Mech. Eng. , vol.135 , pp. 229-241
    • Shu, C.1    Khoo, B.C.2    Chew, Y.T.3    Yeo, K.S.4
  • 25
    • 0029724421 scopus 로고    scopus 로고
    • Differential quadrature method in computational mechanics: a review
    • Bert C.W., Malik M. Differential quadrature method in computational mechanics: a review. Appl. Mech. Rev. 1996, 49:1-28.
    • (1996) Appl. Mech. Rev. , vol.49 , pp. 1-28
    • Bert, C.W.1    Malik, M.2
  • 26
    • 0031104258 scopus 로고    scopus 로고
    • Implementation of clamped and simply supported boundary conditions in the GDQ free vibration analysis of beams and plates
    • Shu C., Du H. Implementation of clamped and simply supported boundary conditions in the GDQ free vibration analysis of beams and plates. Int. J. Solids Struct. 1997, 34:819-835.
    • (1997) Int. J. Solids Struct. , vol.34 , pp. 819-835
    • Shu, C.1    Du, H.2
  • 27
    • 0001782498 scopus 로고    scopus 로고
    • Vibration analysis of continuous systems by differential transformation
    • Malik M., Huy Dang H. Vibration analysis of continuous systems by differential transformation. Appl. Math. Comput. 1998, 96:17-26.
    • (1998) Appl. Math. Comput. , vol.96 , pp. 17-26
    • Malik, M.1    Huy Dang, H.2
  • 28
    • 77955570110 scopus 로고    scopus 로고
    • Meixner-Type results for Riordan arrays and associated integer sequences, Section 6: the Boubaker polynomials
    • Barry P., Hennessy A. Meixner-Type results for Riordan arrays and associated integer sequences, Section 6: the Boubaker polynomials. J. Integer Seq. 2010, 13:1-34.
    • (2010) J. Integer Seq. , vol.13 , pp. 1-34
    • Barry, P.1    Hennessy, A.2
  • 29
    • 78449292894 scopus 로고    scopus 로고
    • A Boubaker Polynomials Expansion Scheme solution to random Love equation in the case of a rational kernel
    • Agida M., Kumar A.S. A Boubaker Polynomials Expansion Scheme solution to random Love equation in the case of a rational kernel. El. J. Theor. Phys. 2010, 7:319-326.
    • (2010) El. J. Theor. Phys. , vol.7 , pp. 319-326
    • Agida, M.1    Kumar, A.S.2
  • 30
    • 77950188711 scopus 로고    scopus 로고
    • Analytical solutions to the pulsed Klein-Gordon equation using Modified Variational Iteration Method (MVIM) and Boubaker Polynomials Expansion Scheme (BPES)
    • Yildirim A., Mohyud-Din S.T., Zhang D.H. Analytical solutions to the pulsed Klein-Gordon equation using Modified Variational Iteration Method (MVIM) and Boubaker Polynomials Expansion Scheme (BPES). Comput. Math. Appl. 2010, 10.1016/j.camwa.2009.12.026.
    • (2010) Comput. Math. Appl.
    • Yildirim, A.1    Mohyud-Din, S.T.2    Zhang, D.H.3
  • 32
    • 56549120277 scopus 로고    scopus 로고
    • A Boubaker polynomials solution to heat equation for monitoring A3 point evolution during resistance spot welding
    • Slama S., Bouhafs M., Ben Mahmoud K.B. A Boubaker polynomials solution to heat equation for monitoring A3 point evolution during resistance spot welding. Int. J. Heat Technol. 2008, 26(2):141-146.
    • (2008) Int. J. Heat Technol. , vol.26 , Issue.2 , pp. 141-146
    • Slama, S.1    Bouhafs, M.2    Ben Mahmoud, K.B.3
  • 33
    • 70349265992 scopus 로고    scopus 로고
    • Cut-off cooling velocity profiling inside a keyhole model using the Boubaker polynomials expansion scheme
    • Tabatabaei S., Zhao T., Awojoyogbe O., Moses F. Cut-off cooling velocity profiling inside a keyhole model using the Boubaker polynomials expansion scheme. Int. J. Heat Mass Transfer 2009, 45:1247-1255.
    • (2009) Int. J. Heat Mass Transfer , vol.45 , pp. 1247-1255
    • Tabatabaei, S.1    Zhao, T.2    Awojoyogbe, O.3    Moses, F.4
  • 34
    • 70349490601 scopus 로고    scopus 로고
    • A new parameter: an ABACUS for optimizing functional materials using the Boubaker polynomials expansion scheme
    • Fridjine S., Amlouk M. A new parameter: an ABACUS for optimizing functional materials using the Boubaker polynomials expansion scheme. Mod. Phys. Lett. B 2009, 23:2179-2182.
    • (2009) Mod. Phys. Lett. B , vol.23 , pp. 2179-2182
    • Fridjine, S.1    Amlouk, M.2
  • 35
    • 70350423094 scopus 로고    scopus 로고
    • Experimental and theoretical cooling velocity profile inside laser welded metals using keyhole approximation and Boubaker polynomials expansion
    • Belhadj A., Bessrour J., Bouhafs M., Barrallier L. Experimental and theoretical cooling velocity profile inside laser welded metals using keyhole approximation and Boubaker polynomials expansion. J. Therm. Anal. Calorimetry 2009, 97:911-920.
    • (2009) J. Therm. Anal. Calorimetry , vol.97 , pp. 911-920
    • Belhadj, A.1    Bessrour, J.2    Bouhafs, M.3    Barrallier, L.4
  • 36
    • 77958110679 scopus 로고    scopus 로고
    • An analytical solution to applied mathematics-related Love's equation using the Boubaker Polynomials Expansion Scheme
    • Kumar A.S. An analytical solution to applied mathematics-related Love's equation using the Boubaker Polynomials Expansion Scheme. J. Franklin Inst. 2010, 347:1755-1761.
    • (2010) J. Franklin Inst. , vol.347 , pp. 1755-1761
    • Kumar, A.S.1
  • 37
    • 78650161444 scopus 로고    scopus 로고
    • The stability of the Boubaker polynomials expansion scheme (BPES)-based solution to Lotka-Volterra problem
    • Milgram A. The stability of the Boubaker polynomials expansion scheme (BPES)-based solution to Lotka-Volterra problem. J. Theor. Biol. 2011, 271:157-158.
    • (2011) J. Theor. Biol. , vol.271 , pp. 157-158
    • Milgram, A.1
  • 38
    • 57649107851 scopus 로고    scopus 로고
    • A two-dimensional layerwise-differential quadrature static analysis of thick laminated composite circular arches
    • Malekzadeh P. A two-dimensional layerwise-differential quadrature static analysis of thick laminated composite circular arches. Appl. Math. Model. 2009, 33:850-1861.
    • (2009) Appl. Math. Model. , vol.33 , pp. 850-1861
    • Malekzadeh, P.1
  • 39
    • 55549085235 scopus 로고    scopus 로고
    • Modeling of water surface profile in subterranean channel by differential quadrature method (DQM)
    • Robati A., Barani G.A. Modeling of water surface profile in subterranean channel by differential quadrature method (DQM). Appl. Math. Model. 2009, 33:1295-1305.
    • (2009) Appl. Math. Model. , vol.33 , pp. 1295-1305
    • Robati, A.1    Barani, G.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.