//Worksheet formula to manage looping

=LET(
    T₊,         SEQUENCE(11, 1, 0, 1),
    T,          DROP(T₊, -1),
    τ,          SEQUENCE(1 / δt, 1, 0, δt),
    calculated, SCAN(1, T, LAMBDA(y₀, t, REDUCE(y₀, t + τ, RungaKutta4λ(Dλ)))),
    calcs,      VSTACK(1, calculated),
    exact,      f(T₊),
    HSTACK(T₊, calcs, exact, (exact - calcs) / exact)
)

//Lambda function passed to RungaKutta4λ to evaluate derivatives

Dλ(y,t)
= LAMBDA(y,t, t * SQRT(y))

//Curried Lambda function with derivative function D and y, t as parameters

RungaKutta4λ(Dλ)
= LAMBDA(D,
      LAMBDA(yᵣ, tᵣ,
          LET(
              δy₁,   δt * D(yᵣ, tᵣ),
              δy₂,   δt * D(yᵣ + δy₁ / 2, tᵣ + δt / 2),
              δy₃,   δt * D(yᵣ + δy₂ / 2, tᵣ + δt / 2),
              δy₄,   δt * D(yᵣ + δy₃, tᵣ + δt),
              yᵣ₊₁,  yᵣ + (δy₁ + 2 * δy₂ + 2 * δy₃ + δy₄) / 6,
              yᵣ₊₁
          )
      )
  )

//Lambda function returning the exact solution

f(t)
= LAMBDA(t, (1/16) * (t^2 + 4)^2 )