Theorems · Theorem · ordinary differential equations

ODE.FunSpace.next_apply

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : ℝ → E → E} {tmin tmax : ℝ}
  {t₀ : ↑(Set.Icc tmin tmax)} {x₀ x : E} {a r L K : NNReal} (hf : IsPicardLindelof f t₀ x₀ a r L K)
  (hx : x ∈ Metric.closedBall x₀ ↑r) (α : ODE.FunSpace t₀ x₀ r L) {t : ↑(Set.Icc tmin tmax)},
  (ODE.FunSpace.next hf hx α).toFun t = ODE.picard f (↑t₀) x α.compProj ↑t

Defined in

Mathlib.Analysis.ODE.PicardLindelof

Cited by

5 results in Mathlib

Foundations

Depth 264 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace