Initial release

engine/plugins/solvers/rk4.lua

@@ -0,0 +1,54 @@
+-- rk4.lua: Classic 4th-order Runge-Kutta solver
+-- 4 NFE per step, excellent accuracy for smooth flows.
+
+solver = {
+    name        = "rk4",
+    display     = "RK4 (4 NFE)",
+    description = "Classic 4th-order Runge-Kutta",
+    nfe         = 4,
+    order       = 4,
+    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
+    local t_mid = t_curr - 0.5 * dt
+
+    -- k1 = vt (already evaluated)
+    -- Save k1 and original xt
+    local k1 = {}
+    local xt_orig = {}
+    for i = 0, n - 1 do
+        k1[i] = vt[i]
+        xt_orig[i] = xt[i]
+    end
+
+    -- k2: evaluate at midpoint using k1
+    for i = 0, n - 1 do
+        xt[i] = xt_orig[i] - 0.5 * k1[i] * dt
+    end
+    model_fn(xt, t_mid)
+    local k2 = {}
+    for i = 0, n - 1 do k2[i] = vt_buf[i] end
+
+    -- k3: evaluate at midpoint using k2
+    for i = 0, n - 1 do
+        xt[i] = xt_orig[i] - 0.5 * k2[i] * dt
+    end
+    model_fn(xt, t_mid)
+    local k3 = {}
+    for i = 0, n - 1 do k3[i] = vt_buf[i] end
+
+    -- k4: evaluate at endpoint using k3
+    for i = 0, n - 1 do
+        xt[i] = xt_orig[i] - k3[i] * dt
+    end
+    model_fn(xt, t_prev)
+
+    -- Combine: xt = xt_orig - (k1 + 2*k2 + 2*k3 + k4) * dt / 6
+    for i = 0, n - 1 do
+        xt[i] = xt_orig[i] - (k1[i] + 2*k2[i] + 2*k3[i] + vt_buf[i]) * dt / 6.0
+    end
+end