Geometric Integration via Multi-space

  title={Geometric Integration via Multi-space},
  author={Pilwon Kim and Peter J. Olver}
We outline a general construction of symmetry-preserving numerical schemes for ordinary differential equations. The method of invariantization is based on the equivariant moving frame theory applied to prolonged symmetry group actions on multi-space, which has been proposed as the proper geometric setting for numerical analysis. We explain how to invariantize standard numerical integrators such as the Euler and Runge–Kutta schemes. In favorable situations, the resulting symmetry-preserving… CONTINUE READING

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