HE Yin-nian. Taylor Expansion Method for the Nonlinear Evolution Equations[J]. Applied Mathematics and Mechanics, 2005, 26(4): 481-488.
Citation: HE Yin-nian. Taylor Expansion Method for the Nonlinear Evolution Equations[J]. Applied Mathematics and Mechanics, 2005, 26(4): 481-488.

Taylor Expansion Method for the Nonlinear Evolution Equations

  • Received Date: 2003-12-30
  • Rev Recd Date: 2004-09-24
  • Publish Date: 2005-04-15
  • A new numerical method of integrating the nonlinear evolution equations,namely the Taylor expansion method,was presented.The standard Galerkin method can be viewed as the 0-th order Taylor expansion method;while the nonlinear Galerkin method can be viewed as the 1-st order modified Taylor expansion method.Moreover,the existence of the numerical solution and its convergence rate were proven.Finally,a concrete example,namely the two-dimensional Navier-Stokes equations with a non slip boundary condition,was provided.The result is that the higher order Taylor expansion method is of the higher convergence rate under some assumptions about the regularity of the solution.
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