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Error estimation

Methods with time step adaptation require estimating the error of the solution. The error is then forwarded to algorithms from OrdinaryDiffEq.jl, see documentation.

ManifoldDiffEq.calculate_eest — Method
calculate_eest(M::AbstractManifold, utilde, uprev, u, abstol, reltol, internalnorm, t)

Estimate error of a solution of an ODE on manifold M.

Arguments

  • utilde – point on M for error estimation,
  • uprev – point from before the current step,
  • u – point after the current step`,
  • abstol - abolute tolerance,
  • reltol - relative tolerance,
  • internalnorm – copied internalnorm from the integrator,
  • t – time at which the error is estimated.
source
ManifoldDiffEq.reltol_norm — Method
reltol_norm(M::AbstractManifold, u)

Estimate the fraction d_{min}/eps(number_eltype(u)) where d_{min} is the distance between u, a point on M, and the nearest distinct point on M representable in the representation of u.

source

Literature