메뉴 건너뛰기




Volumn 24, Issue 4, 2011, Pages 559-565

Integrals of Bernstein polynomials: An application for the solution of high even-order differential equations

Author keywords

Bernstein polynomials; High order differential equations; Spectral method

Indexed keywords

BERNSTEIN POLYNOMIAL; EXPLICIT FORMULA; HIGH ORDER; NUMERICAL SOLUTION; ORDER BOUNDARIES; SPECTRAL METHOD; TWO POINT BOUNDARY CONDITIONS;

EID: 78650516844     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aml.2010.11.013     Document Type: Article
Times cited : (118)

References (22)
  • 1
    • 34247379940 scopus 로고    scopus 로고
    • Solutions of differential equations in a Bernstein polynomial basis
    • DOI 10.1016/j.cam.2006.05.002, PII S0377042706003153
    • M.I. Bhatti, and P. Bracken Solutions of differential equations in Bernstein polynomial basis J. Comput. Appl. Math. 205 2007 272 280 (Pubitemid 46636072)
    • (2007) Journal of Computational and Applied Mathematics , vol.205 , Issue.1 , pp. 272-280
    • Idrees Bhatti, M.1    Bracken, P.2
  • 2
    • 0036287075 scopus 로고    scopus 로고
    • Convergence of generalized Bernstein polynomials
    • A. Il'inskii, and S. Ostrovska Convergence of generalized Bernstein polynomials J. Approx. Theory 116 2002 100 112
    • (2002) J. Approx. Theory , vol.116 , pp. 100-112
    • Il'Inskii, A.1    Ostrovska, S.2
  • 3
    • 77950459048 scopus 로고    scopus 로고
    • The moments for q-Bernstein operators in the case ( 0
    • N. Mahmudov The moments for q-Bernstein operators in the case (0 < q < 1 ) Numer. Algorithms 53 2010 439 450
    • (2010) Numer. Algorithms , vol.53 , pp. 439-450
    • Mahmudov, N.1
  • 4
    • 77956063494 scopus 로고    scopus 로고
    • A new approach to the numerical solution of Volterra integral equations by using Bernsteins approximation
    • K. Maleknejad, E. Hashemizadeh, and R. Ezzati A new approach to the numerical solution of Volterra integral equations by using Bernsteins approximation Commun. Nonlinear Sci. Numer. Simul. 16 2011 647 655
    • (2011) Commun. Nonlinear Sci. Numer. Simul. , vol.16 , pp. 647-655
    • Maleknejad, K.1    Hashemizadeh, E.2    Ezzati, R.3
  • 5
    • 60549106684 scopus 로고    scopus 로고
    • The convergence of q-Bernstein polynomials ( 0
    • S. Ostrovska The convergence of q-Bernstein polynomials (0 < q < 1 ) in the complex plane Math. Nachr. 282 2009 243 252
    • (2009) Math. Nachr. , vol.282 , pp. 243-252
    • Ostrovska, S.1
  • 7
    • 34250793932 scopus 로고    scopus 로고
    • A generalization of rational BernsteinBezier curves
    • . Diibyk, and H. Oru A generalization of rational BernsteinBezier curves BIT 47 2007 313 323
    • (2007) BIT , vol.47 , pp. 313-323
    • Diibyk, .1    Oru, H.2
  • 9
    • 0030516403 scopus 로고    scopus 로고
    • On the optimal stability of Bernstein basis
    • R.T. Farouki, and T.N.T. Goodman On the optimal stability of Bernstein basis Math. Comp. 65 1996 1553 1566
    • (1996) Math. Comp. , vol.65 , pp. 1553-1566
    • Farouki, R.T.1    Goodman, T.N.T.2
  • 11
    • 66049087571 scopus 로고    scopus 로고
    • Jacobi spectral Galerkin method for the integrated forms of fourth-order elliptic differential equations
    • E.H. Doha, and A.H. Bhrawy Jacobi spectral Galerkin method for the integrated forms of fourth-order elliptic differential equations Numer. Methods Partial Differential Equations 25 2009 712 739
    • (2009) Numer. Methods Partial Differential Equations , vol.25 , pp. 712-739
    • Doha, E.H.1    Bhrawy, A.H.2
  • 13
    • 0037082968 scopus 로고    scopus 로고
    • On the coefficients of integrated expansions and integrals of ultraspherical polynomials and their applications for solving differential equations
    • E.H. Doha On the coefficients of integrated expansions and integrals of ultraspherical polynomials and their applications for solving differential equations J. Comput. Appl. Math. 139 2002 275 298
    • (2002) J. Comput. Appl. Math. , vol.139 , pp. 275-298
    • Doha, E.H.1
  • 14
    • 0037303151 scopus 로고    scopus 로고
    • Explicit formulae for the coefficients of integrated expansions for Jacobi polynomials and their integrals
    • E.H. Doha Explicit formulae for the coefficients of integrated expansions for Jacobi polynomials and their integrals Integral Transforms Spec. Funct. 14 2003 69 86
    • (2003) Integral Transforms Spec. Funct. , vol.14 , pp. 69-86
    • Doha, E.H.1
  • 16
    • 34250866829 scopus 로고    scopus 로고
    • second ed. John Wiley & sons
    • R. Merris Combinatorics second ed. 2003 John Wiley & sons
    • (2003) Combinatorics
    • Merris, R.1
  • 19
    • 33947178453 scopus 로고    scopus 로고
    • A comparison between the SincGalerkin and the modified decomposition methods for solving two-point boundary value problems
    • M. El-Gamel A comparison between the SincGalerkin and the modified decomposition methods for solving two-point boundary value problems J. Comput. Phys. 223 2007 369 383
    • (2007) J. Comput. Phys. , vol.223 , pp. 369-383
    • El-Gamel, M.1
  • 20
    • 53449090705 scopus 로고    scopus 로고
    • High order accuracy nonpolynomial spline solutions for 2μth order two point boundary value problems
    • M.A. Ramadan, I.F. Lashien, and W.K. Zahra High order accuracy nonpolynomial spline solutions for 2 μth order two point boundary value problems Appl. Math. Comput. 204 2008 920 927
    • (2008) Appl. Math. Comput. , vol.204 , pp. 920-927
    • Ramadan, M.A.1    Lashien, I.F.2    Zahra, W.K.3
  • 21
    • 40149109797 scopus 로고    scopus 로고
    • Septic spline solutions of sixth-order boundary value problems
    • DOI 10.1016/j.cam.2007.04.013, PII S0377042707002038
    • S.S. Siddiqi, and G. Akram Septic spline solutions of sixth-order boundary value problems J. Comput. Appl. Math. 215 2008 288 301 (Pubitemid 351324857)
    • (2008) Journal of Computational and Applied Mathematics , vol.215 , Issue.1 , pp. 288-301
    • Siddiqi, S.S.1    Akram, G.2
  • 22
    • 0035281487 scopus 로고    scopus 로고
    • The numerical solution of sixth-order boundary value problems by the modified decomposition method
    • DOI 10.1016/S0096-3003(99)00224-6, PII S0096300399002246
    • A.M. Wazwaz The numerical solution of sixth-order boundary value problems by the modified decomposition method Appl. Math. Comput. 118 2001 311 325 (Pubitemid 33592923)
    • (2001) Applied Mathematics and Computation , vol.118 , Issue.2-3 , pp. 311-325
    • Wazwaz, A.-M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.