Initial release

engine/plugins/solvers/heun.lua

@@ -0,0 +1,34 @@
+-- heun.lua: Heun's method (improved Euler / explicit trapezoidal)
+-- 2 NFE: evaluate at t_curr, predict, evaluate at t_prev, average.
+
+solver = {
+    name        = "heun",
+    display     = "Heun (2 NFE)",
+    description = "Second-order predictor-corrector",
+    nfe         = 2,
+    order       = 2,
+    needs_model = true,
+    stateful    = false,
+    stochastic  = false,
+}
+
+function step(xt, vt, t_curr, t_prev, n, model_fn, vt_buf)
+    local dt = t_curr - t_prev
+
+    -- Predict: xt_pred = xt - vt * dt
+    for i = 0, n - 1 do
+        xt[i] = xt[i] - vt[i] * dt
+    end
+
+    -- Correct: evaluate at (xt_pred, t_prev)
+    model_fn(xt, t_prev)
+
+    -- Average: xt = xt + 0.5 * (vt_buf - vt) * dt
+    -- Note: xt is already xt_pred = xt_orig - vt * dt
+    -- We want: xt_orig - 0.5*(vt + vt_buf)*dt
+    -- = (xt + vt*dt) - 0.5*(vt + vt_buf)*dt
+    -- = xt + 0.5*(vt - vt_buf)*dt
+    for i = 0, n - 1 do
+        xt[i] = xt[i] + 0.5 * (vt[i] - vt_buf[i]) * dt
+    end
+end