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2 results

  • POSITIVE SOLUTIONS OF A SECOND-ORDER NEUMANN BOUNDARY VALUE PROBLEM WITH A PARAMETER

  • Part of
  • YANG-WEN ZHANG, HONG-XU LI
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 86 / Issue 2 / October 2012
    Published online by Cambridge University Press:
    16 March 2012, pp. 244-253
    Print publication:
    October 2012
    • Article
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  • In this paper, we consider the Neumann boundary value problem with a parameter λ∈(0,∞): By using fixed point theorems in a cone, we obtain some existence, multiplicity and nonexistence results for positive solutions in terms of different values of λ. We also prove an existence and uniqueness theorem and show the continuous dependence of solutions on the parameter λ.

  • Mixed Fourier-Jacobi Spectral Method for Two-Dimensional Neumann Boundary Value Problems

  • Xu-Hong Yu, Zhong-Qing Wang
  • Journal:
    East Asian Journal on Applied Mathematics / Volume 1 / Issue 3 / August 2011
    Published online by Cambridge University Press:
    28 May 2015, pp. 284-296
    Print publication:
    August 2011

  • In this paper, we propose a mixed Fourier-Jacobi spectral method for two dimensional Neumann boundary value problem. This method differs from the classical spectral method. The homogeneous Neumann boundary condition is satisfied exactly. Moreover, a tridiagonal matrix is employed, instead of the full stiffness matrix encountered in the classical variational formulation. For analyzing the numerical error, we establish the mixed Fourier-Jacobi orthogonal approximation. The convergence of proposed scheme is proved. Numerical results demonstrate the efficiency of this approach.