메뉴 건너뛰기




Volumn 181, Issue 11, 2010, Pages 1868-1872

Non-polynomial spline method for solving Bratu's problem

Author keywords

Bratu's problem; Convergence analysis; Non polynomial spline; Two point boundary value problem

Indexed keywords

APPROXIMATE SOLUTION; B-SPLINE; BRATU'S PROBLEM; CONVERGENCE ANALYSIS; DECOMPOSITION METHODS; GRID POINTS; MAXIMUM ABSOLUTE ERROR; NON-POLYNOMIAL SPLINE; POLYNOMIAL SPLINES; STEP SIZE; TRIDIAGONAL MATRICES; TWO-POINT BOUNDARY VALUE PROBLEM;

EID: 77956262110     PISSN: 00104655     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cpc.2010.08.004     Document Type: Article
Times cited : (83)

References (30)
  • 2
    • 2342505312 scopus 로고    scopus 로고
    • Application of a Mickens finite-difference scheme to the cylindrical Bratu-Gelfand problem
    • R. Buckmire Application of a Mickens finite-difference scheme to the cylindrical Bratu-Gelfand problem Numer. Methods Partial Differential Equations 20 3 2004 327 337
    • (2004) Numer. Methods Partial Differential Equations , vol.20 , Issue.3 , pp. 327-337
    • Buckmire, R.1
  • 3
    • 0036751359 scopus 로고    scopus 로고
    • The Liouville-Bratu-Gelfand problem for radial operators
    • J. Jacobsen, and K. Schmitt The Liouville-Bratu-Gelfand problem for radial operators J. Differential Equations 184 2002 283 298
    • (2002) J. Differential Equations , vol.184 , pp. 283-298
    • Jacobsen, J.1    Schmitt, K.2
  • 4
    • 0012166933 scopus 로고    scopus 로고
    • Numerical continuation and the Gelfand problem
    • J.S. McGough Numerical continuation and the Gelfand problem Appl. Math. Comput. 89 1998 225 239
    • (1998) Appl. Math. Comput. , vol.89 , pp. 225-239
    • McGough, J.S.1
  • 5
    • 33745801140 scopus 로고    scopus 로고
    • From the fitting techniques to accurate schemes for the Liouville-Bratu-Gelfand problem
    • A.S. Mounim, and B.M. de Dormale From the fitting techniques to accurate schemes for the Liouville-Bratu-Gelfand problem Numer. Methods Partial Differential Equations 22 4 2006 761 775
    • (2006) Numer. Methods Partial Differential Equations , vol.22 , Issue.4 , pp. 761-775
    • Mounim, A.S.1    De Dormale, B.M.2
  • 6
    • 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. 142 2003 189 200
    • (2003) Appl. Math. Comput. , vol.142 , pp. 189-200
    • Boyd, J.P.1
  • 8
    • 33646364314 scopus 로고    scopus 로고
    • An efficient method for solving Bratu equations
    • M.I. 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.I.1    Hamdan, A.2
  • 9
    • 25844478165 scopus 로고    scopus 로고
    • An analytic approach to solve multiple solutions of a strongly nonlinear problem
    • S. Li, and S.J. 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.J.2
  • 10
    • 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
  • 11
    • 33645972898 scopus 로고    scopus 로고
    • Some asymptotic methods for strongly nonlinear equations
    • J.H. He Some asymptotic methods for strongly nonlinear equations Internat. J. Modern Phys. B 20 10 2006 1141 1199
    • (2006) Internat. J. Modern Phys. B , vol.20 , Issue.10 , pp. 1141-1199
    • He, J.H.1
  • 12
    • 40549127760 scopus 로고    scopus 로고
    • Variational approach to the Bratu's problem
    • J.H. He Variational approach to the Bratu's problem J. Phys.: Conf. Ser. 96 2008 012087
    • (2008) J. Phys.: Conf. Ser. , vol.96 , pp. 012087
    • He, J.H.1
  • 13
    • 34848900880 scopus 로고    scopus 로고
    • A general approach to obtain series solutions of nonlinear differential equations
    • S. Liao, and Y. Tan A general approach to obtain series solutions of nonlinear differential equations Stud. Appl. Math. 119 2007 297 354
    • (2007) Stud. Appl. Math. , vol.119 , pp. 297-354
    • Liao, S.1    Tan, Y.2
  • 14
    • 0005338184 scopus 로고    scopus 로고
    • An algorithm for solving boundary value problems
    • E. Deeba, S.A. Khuri, and S. Xie An algorithm for solving boundary value problems J. Comput. Phys. 159 2000 125 138
    • (2000) J. Comput. Phys. , vol.159 , pp. 125-138
    • Deeba, E.1    Khuri, S.A.2    Xie, S.3
  • 15
    • 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. 147 2004 131 136
    • (2004) Appl. Math. Comput. , vol.147 , pp. 131-136
    • Khuri, S.A.1
  • 16
    • 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 1 2003 1 7
    • (2003) Electron. J. South Afr. Math. Sci. , vol.3 , Issue.1 , pp. 1-7
    • Aregbesola, Y.A.S.1
  • 17
    • 72149102881 scopus 로고    scopus 로고
    • Applying differential transformation method to the one-dimensional planar Bratu problem
    • I.H.A.H. Hassan, and V.S. 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.H.A.H.1    Erturk, V.S.2
  • 18
    • 34848838599 scopus 로고    scopus 로고
    • Non-polynomial spline for solution of boundary-value problems in plate deflection theory
    • J. Rashidinia, and R. Jalilian Non-polynomial spline for solution of boundary-value problems in plate deflection theory Int. J. Comput. Math. 84 2007 1483 1494
    • (2007) Int. J. Comput. Math. , vol.84 , pp. 1483-1494
    • Rashidinia, J.1    Jalilian, R.2
  • 19
    • 34248175663 scopus 로고    scopus 로고
    • Non-polynomial spline methods for the solution of a system of obstacle problems
    • J. Rashidinia, R. Jalilian, and R. Mohammadi Non-polynomial spline methods for the solution of a system of obstacle problems Appl. Math. Comput. 188 2007 1984 1990
    • (2007) Appl. Math. Comput. , vol.188 , pp. 1984-1990
    • Rashidinia, J.1    Jalilian, R.2    Mohammadi, R.3
  • 20
    • 0028762856 scopus 로고
    • Smooth approximation for the solution of a fourth-order boundary value problem based on non-polynomial splines
    • M. Van Daele, G. Vanden Berghe, and H.A. De Meyer Smooth approximation for the solution of a fourth-order boundary value problem based on non-polynomial splines J. Comput. Appl. Math. 51 1994 383 394
    • (1994) J. Comput. Appl. Math. , vol.51 , pp. 383-394
    • Van Daele, M.1    Vanden Berghe, G.2    De Meyer, H.A.3
  • 21
    • 55549099933 scopus 로고    scopus 로고
    • Quintic non-polynomial spline solutions for fourth order boundary value problem
    • M. Ramadan, I. Lashien, and W. Zahra Quintic non-polynomial spline solutions for fourth order boundary value problem Commun. Nonlinear Sci. Numer. Simul. 14 2009 1105 1114
    • (2009) Commun. Nonlinear Sci. Numer. Simul. , vol.14 , pp. 1105-1114
    • Ramadan, M.1    Lashien, I.2    Zahra, W.3
  • 22
    • 38049159746 scopus 로고    scopus 로고
    • Family of numerical methods based on non-polynomial splines for solution of contact problems
    • S. ul Islam, I.A. Tirmizi, F. Haq, and S.K. Taseer Family of numerical methods based on non-polynomial splines for solution of contact problems Commun. Nonlinear Sci. Numer. Simul. 13 2008 1448 1460
    • (2008) Commun. Nonlinear Sci. Numer. Simul. , vol.13 , pp. 1448-1460
    • Ul Islam, S.1    Tirmizi, I.A.2    Haq, F.3    Taseer, S.K.4
  • 23
    • 33749531922 scopus 로고    scopus 로고
    • Solution of sixth order boundary value problems using non-polynomial spline technique
    • G. Akram, and S. Siddiqi Solution of sixth order boundary value problems using non-polynomial spline technique Appl. Math. Comput. 181 2006 708 720
    • (2006) Appl. Math. Comput. , vol.181 , pp. 708-720
    • Akram, G.1    Siddiqi, S.2
  • 24
    • 0019178652 scopus 로고
    • Quintic spline solutions of boundary value problems
    • R.A. Usmani, and S.A. Warsi Quintic spline solutions of boundary value problems Comput. Math. Appl. 6 1980 197 203
    • (1980) Comput. Math. Appl. , vol.6 , pp. 197-203
    • Usmani, R.A.1    Warsi, S.A.2
  • 25
    • 52049118060 scopus 로고    scopus 로고
    • New smoother to enhance multigrid-based methods for Bratu problem
    • A. Mohsen, L.F. Sedeek, and S.A. Mohamed New smoother to enhance multigrid-based methods for Bratu problem Appl. Math. Comput. 204 2008 325 339
    • (2008) Appl. Math. Comput. , vol.204 , pp. 325-339
    • Mohsen, A.1    Sedeek, L.F.2    Mohamed, S.A.3
  • 26
    • 33748097811 scopus 로고    scopus 로고
    • Higher-order finite-difference methods for nonlinear second-order two-point boundary-value problems
    • I.A. Tirmizi, and E.H. Twizell Higher-order finite-difference methods for nonlinear second-order two-point boundary-value problems Appl. Math. Lett. 15 2002 897 902
    • (2002) Appl. Math. Lett. , vol.15 , pp. 897-902
    • Tirmizi, I.A.1    Twizell, E.H.2
  • 27
    • 0001575024 scopus 로고
    • Properties of some tridiagonal matrices and their application to boundary value problems
    • C.F. Fischer, and R.A. Usmani Properties of some tridiagonal matrices and their application to boundary value problems SIAM J. Numer. Anal. 6 1969 127 142
    • (1969) SIAM J. Numer. Anal. , vol.6 , pp. 127-142
    • Fischer, C.F.1    Usmani, R.A.2
  • 29
    • 0016440637 scopus 로고
    • Numerical solution of some ordinary differential equations occurring in plate deflection theory
    • R.A. Usmani, and M.J. Marsden Numerical solution of some ordinary differential equations occurring in plate deflection theory J. Engrg. Math. 9 1975 1 10
    • (1975) J. Engrg. Math. , vol.9 , pp. 1-10
    • Usmani, R.A.1    Marsden, M.J.2
  • 30
    • 0039647244 scopus 로고
    • Numerical solution of a fourth-order ordinary differential equation
    • M. Jain, S. Iyengar, and J. Saldanha Numerical solution of a fourth-order ordinary differential equation J. Engrg. Math. 11 1977 373 380
    • (1977) J. Engrg. Math. , vol.11 , pp. 373-380
    • Jain, M.1    Iyengar, S.2    Saldanha, J.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.