Geometric integration using discrete

  title={Geometric integration using discrete},
  author={gradientsRobert and Ian G McLachlan and G. R. W. Quispel and Nicolas Robidoux},
This paper discusses the discrete analogue of the gradient of a function and shows how discrete gradients can be used in the numerical integration of ordinary diieren-tial equations (ODE's). Given an ODE and one or more rst integrals (i.e., constants of the motion) and/or Lyapunov functions, it is shown that the ODE can be rewritten as a `linear-gradient system.' Discrete gradients are used to construct discrete approximations to the ODE which preserve the rst integrals and Lyapunov functions… CONTINUE READING


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