Open Science Research Excellence
@article{(International Science Index):,
  title    = {Iteration Acceleration for Nonlinear Coupled Parabolic-Hyperbolic System},
  author    = {Xia Cui and  Guang-wei Yuan and  Jing-yan Yue},
  country   = {},
  abstract  = {A Picard-Newton iteration method is studied to accelerate the numerical solution procedure of a class of two-dimensional nonlinear coupled parabolic-hyperbolic system. The Picard-Newton iteration is designed by adding higher-order terms of small quantity to an existing Picard iteration. The discrete functional analysis and inductive hypothesis reasoning techniques are used to overcome difficulties coming from nonlinearity and coupling, and theoretical analysis is made for the convergence and approximation properties of the iteration scheme. The Picard-Newton iteration has a quadratic convergent ratio, and its solution has second order spatial approximation and first order temporal approximation to the exact solution of the original problem. Numerical tests verify the results of the theoretical analysis, and show the Picard-Newton iteration is more efficient than the Picard iteration.
    journal   = {International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering},  volume    = {5},
  number    = {9},
  year      = {2011},
  pages     = {1496 - 1501},
  ee        = {},
  url       = {},
  bibsource = {},
  issn      = {eISSN:1307-6892},
  publisher = {World Academy of Science, Engineering and Technology},
  index     = {International Science Index 57, 2011},