Data commit

Task/Runge-Kutta-method/Excel/runge-kutta-method.excel

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+//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 )