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Volumn 217, Issue 12, 2011, Pages 5553-5565

One-point pseudospectral collocation for the one-dimensional Bratu equation

Author keywords

Bratu equation; Chebyshev polynomial; Collocation; Orthogonal collocation; Pseudospectral

Indexed keywords

BRATU EQUATION; CHEBYSHEV POLYNOMIAL; COLLOCATION; ORTHOGONAL COLLOCATION; PSEUDOSPECTRAL;

EID: 79551642119     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2010.12.029     Document Type: Article
Times cited : (54)

References (27)
  • 1
    • 77951030788 scopus 로고    scopus 로고
    • Numerical solution of Bratu problem using the method of weighted residual
    • Y.A.S. Aregbesola Numerical solution of Bratu problem using the method of weighted residual Electron. J. South. Afr. Math. Sci. 3 2003 1 7
    • (2003) Electron. J. South. Afr. Math. Sci. , vol.3 , pp. 1-7
    • Aregbesola, Y.A.S.1
  • 3
    • 0023015595 scopus 로고
    • An analytical and numerical study of the two-dimensional Bratu equation
    • J.P. Boyd An analytical and numerical study of the two-dimensional Bratu equation J. Sci. Comput. 1 1985 183 206
    • (1985) J. Sci. Comput. , vol.1 , pp. 183-206
    • Boyd, J.P.1
  • 4
    • 0001195344 scopus 로고
    • Chebyshev and Legendre spectral methods in algebraic manipulation languages
    • J.P. Boyd Chebyshev and Legendre spectral methods in algebraic manipulation languages J. Symb. Comput. 16 1993 377 399
    • (1993) J. Symb. Comput. , vol.16 , pp. 377-399
    • Boyd, J.P.1
  • 5
    • 0010091233 scopus 로고    scopus 로고
    • Global approximations to the principal real-valued branch of the Lambert W-function
    • J.P. Boyd Global approximations to the principal real-valued branch of the Lambert W-function Appl. Math. Lett. 11 1998 27 31 errata: in Eq. (4), 11/36 should be 2 11 / 36
    • (1998) Appl. Math. Lett. , vol.11 , pp. 27-31
    • Boyd, J.P.1
  • 7
    • 0035341740 scopus 로고    scopus 로고
    • Rational Chebyshev spectral methods for unbounded solutions on an infinite interval using polynomial-growth special basis functions
    • J.P. Boyd Rational Chebyshev spectral methods for unbounded solutions on an infinite interval using polynomial-growth special basis functions Comput. Math. Appl. 41 2001 1293 1315
    • (2001) Comput. Math. Appl. , vol.41 , pp. 1293-1315
    • Boyd, J.P.1
  • 8
    • 0038521511 scopus 로고    scopus 로고
    • Chebyshev polynomial expansions for simultaneous approximation of two branches of a function with application to the one-dimensional Bratu equation
    • J.P. Boyd Chebyshev polynomial expansions for simultaneous approximation of two branches of a function with application to the one-dimensional Bratu equation Appl. Math. Comput. 143 2002 189 200
    • (2002) Appl. Math. Comput. , vol.143 , pp. 189-200
    • Boyd, J.P.1
  • 9
    • 0010950704 scopus 로고
    • Sur les équations intégrales non linéaires
    • G. Bratu Sur les équations intégrales non linéaires Bull. Soc. Math. France 43 1914 113 142
    • (1914) Bull. Soc. Math. France , vol.43 , pp. 113-142
    • Bratu, G.1
  • 10
    • 77955279417 scopus 로고    scopus 로고
    • A variational iteration method for solving troeschs problem
    • S.-H. Chang A variational iteration method for solving troeschs problem J. Comput. Appl. Math. 234 2010 3043 3047
    • (2010) J. Comput. Appl. Math. , vol.234 , pp. 3043-3047
    • Chang, S.-H.1
  • 12
    • 0005338184 scopus 로고    scopus 로고
    • An algorithm for solving boundary value problems
    • E. Deeba, S. Khuri, S. Xie, An algorithm for solving boundary value problems, J. Comput. Phys. 159 (19) 125-138.
    • J. Comput. Phys. , vol.159 , Issue.19 , pp. 125-138
    • Deeba, E.1    Khuri, S.2    Xie, S.3
  • 14
    • 0016450765 scopus 로고
    • Orthogonal collocation in chemical-reaction engineering
    • B.A. Finlayson Orthogonal collocation in chemical-reaction engineering Catal. Rev. Sci. Eng. 10 1974 69 138
    • (1974) Catal. Rev. Sci. Eng. , vol.10 , pp. 69-138
    • Finlayson, B.A.1
  • 15
    • 0000247179 scopus 로고
    • Some problems in the theory of quasi-linear equations
    • I.M. Gelfand Some problems in the theory of quasi-linear equations Trans. Amer. Math. Soc. Ser. 2 1963 295 381
    • (1963) Trans. Amer. Math. Soc. Ser. , vol.2 , pp. 295-381
    • Gelfand, I.M.1
  • 16
    • 72149102881 scopus 로고    scopus 로고
    • Applying differential transformation method to the one-dimensional planar Bratu problem
    • I. Hassan, and V. Erturk Applying differential transformation method to the one-dimensional planar Bratu problem Int. J. Contemp. Math. Sci. 2 2007 1493 1504
    • (2007) Int. J. Contemp. Math. Sci. , vol.2 , pp. 1493-1504
    • Hassan, I.1    Erturk, V.2
  • 17
    • 33645972898 scopus 로고    scopus 로고
    • Some asymptotic methods for strongly nonlinear equations
    • J.H. He Some asymptotic methods for strongly nonlinear equations Int. J. Mod. Phys. B 20 2006 1141 1199
    • (2006) Int. J. Mod. Phys. B , vol.20 , pp. 1141-1199
    • He, J.H.1
  • 19
    • 28244446638 scopus 로고    scopus 로고
    • A numerical algorithm for solving the Troesch's problem
    • S.A. Khuri A numerical algorithm for solving the Troesch's problem Int. J. Comput. Math. 80 2003 493 498
    • (2003) Int. J. Comput. Math. , vol.80 , pp. 493-498
    • Khuri, S.A.1
  • 20
    • 0141525039 scopus 로고    scopus 로고
    • A new approach to Bratu's problem
    • S.A. Khuri A new approach to Bratu's problem Appl. Math. Comput. 1477 2004 131 136
    • (2004) Appl. Math. Comput. , vol.1477 , pp. 131-136
    • Khuri, S.A.1
  • 21
    • 25844478165 scopus 로고    scopus 로고
    • An analytic approach to solve multiple solutions of a strongly nonlinear problem
    • S. Li, and S. Liao An analytic approach to solve multiple solutions of a strongly nonlinear problem Appl. Math. Comput. 169 2005 854 865
    • (2005) Appl. Math. Comput. , vol.169 , pp. 854-865
    • Li, S.1    Liao, S.2
  • 22
    • 33745801140 scopus 로고    scopus 로고
    • From the fitting techniques to accurate schemes for the Liouville-Bratu-Gelfand problem
    • A. Mounim, and B. de Dormale From the fitting techniques to accurate schemes for the Liouville-Bratu-Gelfand problem Numer. Meth. Part. Diff. Eq. 22 2006 761 775
    • (2006) Numer. Meth. Part. Diff. Eq. , vol.22 , pp. 761-775
    • Mounim, A.1    De Dormale, B.2
  • 23
    • 37349011714 scopus 로고
    • On the conversion of boundary-value problems into stable initial-value problems via several invariant imbedding algorithms
    • M.R. Scott On the conversion of boundary-value problems into stable initial-value problems via several invariant imbedding algorithms A.K. Aziz, Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations 1975 Academic Press New York 89 146
    • (1975) Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations , pp. 89-146
    • Scott, M.R.1
  • 24
    • 33749553239 scopus 로고
    • A systematized collection of codes for solving two-point boundary-value problems on the conversion of boundary-value problems into stable initial-value problems via several invariant imbedding algorithms
    • M.R. Scott, and H.A. Watts A systematized collection of codes for solving two-point boundary-value problems on the conversion of boundary-value problems into stable initial-value problems via several invariant imbedding algorithms L. Lapidus, W.E. Schiesser, Numerical Methods for Differential Systems 1976 Academic Press New York
    • (1976) Numerical Methods for Differential Systems
    • Scott, M.R.1    Watts, H.A.2
  • 25
    • 0001786527 scopus 로고
    • Computational solution of linear two-point boundary value problems via orthonormalization
    • M.R. Scott, and H.A. Watts Computational solution of linear two-point boundary value problems via orthonormalization SIAM J. Numer. Anal. 14 1977 40 70
    • (1977) SIAM J. Numer. Anal. , vol.14 , pp. 40-70
    • Scott, M.R.1    Watts, H.A.2
  • 26
    • 33646364314 scopus 로고    scopus 로고
    • An efficient method for solving Bratu equations
    • M. Syam, and A. Hamdan An efficient method for solving Bratu equations Appl. Math. Comput. 176 2006 704 713
    • (2006) Appl. Math. Comput. , vol.176 , pp. 704-713
    • Syam, M.1    Hamdan, A.2
  • 27
    • 20444478300 scopus 로고    scopus 로고
    • Adomian decomposition method for a reliable treatment of the Bratu-type equations
    • A.M. Wazwaz Adomian decomposition method for a reliable treatment of the Bratu-type equations Appl. Math. Comput. 166 2005 652 663
    • (2005) Appl. Math. Comput. , vol.166 , pp. 652-663
    • Wazwaz, A.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.