非线性双曲型方程的拟谱方法

Pseudospectral Method for Nonlinear Hyperbolic Equations

本文讨论一类非线性双曲型方程的拟谱方法，构造了半离散和全离散的Ｆｏｕｒｉｅｒ拟谱格式并得到了最优误差估计。本文介绍的方法在计算时不需要数值积分并可应用快速Ｆｏｕ－ｒｉｅｒ变换，减少计算量，如果原微分方程的解无限可微，则近似解具有无穷阶收敛性。

Pseudospectral method for a class of nonlinear hyperbolic equations is discussed inthis paper,It has constructed the semidiscretc and fully diserete Fourier Pseudospectral schemes and ob-tained the optimum error estimates. The method of introduetion in the paper doesn't need numerial integration and can applies fast fou-rier transformation to reduces coniputation,If the solution of original equation is infinite differentiable,then the solution of approximation has infinite ordinal convergence.