Small-stencil Padé schemes to solve nonlinear evolution equations

@article{Ruxun2005SmallstencilPS,
  title={Small-stencil Pad{\'e} schemes to solve nonlinear evolution equations},
  author={Liu Ru-xun and Wu Ling-ling},
  journal={Applied Mathematics and Mechanics},
  year={2005},
  volume={26},
  pages={872-881}
}
A set of small-stencil new Padé schemes with the same denominator are presented to solve high-order nonlinear evolution equations. Using this scheme, the fourth-order precision can not only be kept, but also the final three-diagonal discrete systems are solved by simple Doolittle methods, or ODE systems by Runge-Kutta technique. Numerical samples show that the schemes are very satisfactory. And the advantage of the schemes is very clear compared to other finite difference schemes.