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Volumn 17, Issue 4, 2001, Pages 347-368

Numerical methods for fourth-order nonlinear elliptic boundary value problems

Author keywords

Existence comparison theorem; Finite difference system; Fourth order elliptic equations; Monotone iterations; Numerical solutions; Two point boundary problems; Upper and lower solutions

Indexed keywords


EID: 0035397868     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/num.1016     Document Type: Article
Times cited : (26)

References (24)
  • 1
    • 33947175349 scopus 로고
    • On fourth-order boundary value problems arising in beam analysis
    • R. Agarwal, On fourth-order boundary value problems arising in beam analysis, Differential Integral Eqs 2 (1989), 91-110.
    • (1989) Differential Integral Eqs , vol.2 , pp. 91-110
    • Agarwal, R.1
  • 2
    • 0000934317 scopus 로고
    • The method of upper and lower solutions for second, third, fourth and higher order boundary value problems
    • A. Cabada, The method of upper and lower solutions for second, third, fourth and higher order boundary value problems, J Math Anal Appl 185 (1994), 302-320.
    • (1994) J Math Anal Appl , vol.185 , pp. 302-320
    • Cabada, A.1
  • 3
    • 84950192244 scopus 로고
    • Existence and uniqueness theorem for the bending of an elastic beam equation
    • C. P. Gupta, Existence and uniqueness theorem for the bending of an elastic beam equation, Applicable Anal 26 (1988), 289-304.
    • (1988) Applicable Anal , vol.26 , pp. 289-304
    • Gupta, C.P.1
  • 4
    • 84952401788 scopus 로고
    • On the existence of positive solutions of fourth-order ordinary differential equation
    • R. Y. Ma and H. Y. Wang, On the existence of positive solutions of fourth-order ordinary differential equation, Applicable Anal 59 (1995), 225-231.
    • (1995) Applicable Anal , vol.59 , pp. 225-231
    • Ma, R.Y.1    Wang, H.Y.2
  • 5
    • 0031276985 scopus 로고    scopus 로고
    • The method of lower and upper solutions for fourth-order two-point boundary value problems
    • R. Y. Ma, J. H. Zhang, and S. M. Fu, The method of lower and upper solutions for fourth-order two-point boundary value problems, J Math Anal Appl 215 (1997), 415-422.
    • (1997) J Math Anal Appl , vol.215 , pp. 415-422
    • Ma, R.Y.1    Zhang, J.H.2    Fu, S.M.3
  • 6
    • 84968518888 scopus 로고
    • Fourth-order two-point boundary value problem
    • Y. Yang, Fourth-order two-point boundary value problem, Proc Am Math Soc 104 (1988), 175-180.
    • (1988) Proc Am Math Soc , vol.104 , pp. 175-180
    • Yang, Y.1
  • 8
    • 23044520244 scopus 로고    scopus 로고
    • On fourth-order elliptic boundary value problems
    • C. V. Pao, On fourth-order elliptic boundary value problems, Proc Am Math Soc 128 (1999), 1023-1030.
    • (1999) Proc Am Math Soc , vol.128 , pp. 1023-1030
    • Pao, C.V.1
  • 9
    • 0032017567 scopus 로고    scopus 로고
    • Multiplicity results for a fourth-order semilinear problem
    • A. M. Micheletti and A. Pistoia, Multiplicity results for a fourth-order semilinear problem, Non-linear Anal 31 (1998), 895-908.
    • (1998) Non-linear Anal , vol.31 , pp. 895-908
    • Micheletti, A.M.1    Pistoia, A.2
  • 10
    • 84972514100 scopus 로고
    • A note on a semilinear elliptic problem
    • G. Tarantello, A note on a semilinear elliptic problem, Diff Integ Eq 5 (1992), 561-565.
    • (1992) Diff Integ Eq , vol.5 , pp. 561-565
    • Tarantello, G.1
  • 12
    • 0007121464 scopus 로고    scopus 로고
    • Full-order convergence of a mixed finite element method for fourth-order elliptic equations
    • J. Li, Full-order convergence of a mixed finite element method for fourth-order elliptic equations, J Math Anal Appl 230 (1999), 329-349.
    • (1999) J Math Anal Appl , vol.230 , pp. 329-349
    • Li, J.1
  • 13
    • 0001377705 scopus 로고
    • Mildly nonlinear elliptic partial differential equations and their numerical solution, II
    • D. Greenspan and S. V. Parter, Mildly nonlinear elliptic partial differential equations and their numerical solution, II, Numer Math 7 (1965), 129-146.
    • (1965) Numer Math , vol.7 , pp. 129-146
    • Greenspan, D.1    Parter, S.V.2
  • 14
    • 38249039671 scopus 로고
    • Accelerated monotone scheme for finite difference equations concerning steady-state pre-predator interactions
    • A. Leung and D. Murio, Accelerated monotone scheme for finite difference equations concerning steady-state pre-predator interactions, J Comp Appl Math 16 (1986), 333-341.
    • (1986) J Comp Appl Math , vol.16 , pp. 333-341
    • Leung, A.1    Murio, D.2
  • 16
    • 0000976286 scopus 로고
    • Numerical solutions for some coupled systems of nonlinear boundary value problems
    • C. V. Pao, Numerical solutions for some coupled systems of nonlinear boundary value problems, Numer Math 51 (1987), 381-394.
    • (1987) Numer Math , vol.51 , pp. 381-394
    • Pao, C.V.1
  • 17
    • 0000458942 scopus 로고
    • Monotone iterative methods for finite difference system of reaction-diffusion equations
    • C. V. Pao, Monotone iterative methods for finite difference system of reaction-diffusion equations, Numer Math 46 (1985), 571-586.
    • (1985) Numer Math , vol.46 , pp. 571-586
    • Pao, C.V.1
  • 18
    • 84985415686 scopus 로고
    • Finite difference reaction diffusion equations with nonlinear boundary conditions
    • C. V. Pao, Finite difference reaction diffusion equations with nonlinear boundary conditions, Numer Meth Part Diff Eq 11 (1995), 355-374.
    • (1995) Numer Meth Part Diff Eq , vol.11 , pp. 355-374
    • Pao, C.V.1
  • 19
    • 0001377706 scopus 로고
    • Mildly nonlinear elliptic partial differential equations and their numerical solution, I
    • S. V. Parter, Mildly nonlinear elliptic partial differential equations and their numerical solution, I, Numer Math 7 (1965), 113-128.
    • (1965) Numer Math , vol.7 , pp. 113-128
    • Parter, S.V.1
  • 20
    • 0016484851 scopus 로고
    • Numerical methods for singular boundary value problems
    • R. D. Russell and L. F. Shampine, Numerical methods for singular boundary value problems, SIAM J Numer Anal 12 (1975), 13-16.
    • (1975) SIAM J Numer Anal , vol.12 , pp. 13-16
    • Russell, R.D.1    Shampine, L.F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.