A survey on various computational techniques for nonlinear elliptic boundary value problems

In this paper a classification and a survey on numerical techniques for solving nonlinear (quasilinear, semilinear, superlinear, sublinear) elliptic boundary value problems between 2001 and 2006 have been presented and discussed the nature of positive solution of the various problems. The introduction of the methods and results presented by different researchers are summarized.

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[37]  Xionghua Wu,et al.  A Sinc-collocation method with boundary treatment for two-dimensional elliptic boundary value problems , 2006 .

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[42]  Alfonso Castro,et al.  Multiple solutions for a nonlinear Dirichlet problem , 1994 .

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[51]  G. A. Afrouzi,et al.  A computational algorithm for finding positive solutions for a class of superlinear Dirichlet BVP , 2006, Appl. Math. Comput..

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[55]  A. Castro,et al.  A sign-changing solution for a superlinear Dirichlet problem with a reaction term nonzero at zero , 1997 .

[56]  G. A. Afrouzi,et al.  A numerical method for finding positive solutions of a superlinear Dirichlet problem , 2006, Appl. Math. Comput..

[57]  C. V. Pao,et al.  Finite difference reaction diffusion equations with nonlinear boundary conditions , 1995 .

[58]  Yuan-Ming Wang,et al.  Monotone iterative technique for numerical solutions of fourth-order nonlinear elliptic boundary value problems , 2007 .

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