Taylor expansion method for nonlinear evolution equations |
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Authors: | He Yin-nian |
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Institution: | Faculty of Science, Xi'an Jiaotong University, Xi'an 710049, P.R.China |
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Abstract: | 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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Keywords: | nonlinear evolution equation Navier_Stokes equation Taylor expansion method convergence rate |
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