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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Communicated by Zhang Hong-qing and Xu Zheng-fan
Project supported by the National Natural Science Foundation of China (No. 10371095) and the Natural Science Foundation of Shaanxi Province of China (No. 2003 A01)
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Yin-nian, H. Taylor expansion method for nonlinear evolution equations. Appl Math Mech 26, 522–529 (2005). https://doi.org/10.1007/BF02465392
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DOI: https://doi.org/10.1007/BF02465392