Initial release
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-- stork4.lua: STORK 4 — Stabilized Taylor Orthogonal RK (4th order, 1 NFE)
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-- Uses ROCK4 Chebyshev sub-stepping with precomputed coefficients.
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-- Requires companion stork4_constants.lua.
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local C = require("stork4_constants")
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solver = {
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name = "stork4",
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display = "STORK 4",
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description = "4th-order stabilized Taylor-ROCK4 (1 NFE)",
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nfe = 1,
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order = 4,
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needs_model = false,
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stateful = true,
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stochastic = false,
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params = {
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{ key = "substeps", type = "slider", label = "Substeps",
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default = 10, min = 2, max = 50, step = 1,
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hint = "Number of ROCK4 sub-steps (more = more stable)" },
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},
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}
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local velocity_history = {}
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local function rms(data, n)
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local sum = 0
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for i = 0, n-1 do sum = sum + data[i] * data[i] end
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return math.sqrt(sum / n)
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end
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local function has_nan_inf(data, n)
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for i = 0, n-1 do
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local v = data[i]
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if v ~= v or v == math.huge or v == -math.huge then return true end
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end
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return false
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end
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local function compute_derivatives(vt, n)
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local hist = velocity_history
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if #hist == 0 then return 0, nil, nil end
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local v_prev = hist[#hist].vt
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local h1 = hist[#hist].dt
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if h1 == 0 then return 0, nil, nil end
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local dv = {}
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for i = 0, n-1 do dv[i] = (v_prev[i] - vt[i]) / h1 end
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local vt_rms = rms(vt, n)
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local dv_rms = rms(dv, n)
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if vt_rms > 0 and dv_rms * math.abs(h1) > 5 * vt_rms then return 0, nil, nil end
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if #hist < 2 then return 1, dv, nil end
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local v_prev2 = hist[#hist - 1].vt
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local h2 = hist[#hist - 1].dt
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if h2 == 0 then return 1, dv, nil end
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local denom = h1 * h2 * (h1 + h2)
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if math.abs(denom) < 1e-30 then return 1, dv, nil end
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local coeff = 2 / denom
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local d2v = {}
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for i = 0, n-1 do
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d2v[i] = coeff * (v_prev2[i] * h1 - v_prev[i] * (h1 + h2) + vt[i] * h2)
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end
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local d2v_rms = rms(d2v, n)
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if vt_rms > 0 and d2v_rms * h1 * h1 > 5 * vt_rms then return 1, dv, nil end
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return 2, dv, d2v
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end
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local function taylor_approx(vt, order, diff, dv, d2v, n)
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local out = {}
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if order >= 2 and d2v then
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local half_d2 = 0.5 * diff * diff
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for i = 0, n-1 do out[i] = vt[i] + diff * dv[i] + half_d2 * d2v[i] end
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elseif order >= 1 and dv then
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for i = 0, n-1 do out[i] = vt[i] + diff * dv[i] end
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else
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for i = 0, n-1 do out[i] = vt[i] end
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end
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return out
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end
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local function rock4_mdegr(s)
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local mp1 = 1
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for i = 1, C.MS_LEN do
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if C.MS[i] >= s then
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return C.MS[i], i, mp1 - 1
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end
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mp1 = mp1 + C.MS[i] * 2 - 1
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end
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return C.MS[C.MS_LEN], C.MS_LEN, mp1 - 1
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end
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local function rock4_substep(xt, vt, s, t_curr, t_prev, deriv_order, dv, d2v, n)
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local max_rock4 = C.MS[C.MS_LEN]
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if s > max_rock4 then s = max_rock4 end
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local mdeg, mz, mr = rock4_mdegr(s)
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local dt = t_curr - t_prev
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local Y_j_2 = {}; local Y_j_1 = {}; local Y_j = {}
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for i = 0, n-1 do Y_j_2[i] = xt[i]; Y_j_1[i] = xt[i] end
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local ci1 = t_curr
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-- ROCK4 Chebyshev recurrence (1-indexed RECF)
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for j = 1, mdeg do
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if j == 1 then
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local temp1 = -dt * C.RECF[mr + 1]
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ci1 = t_curr + temp1
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for i = 0, n-1 do Y_j_1[i] = xt[i] + temp1 * vt[i] end
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else
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local diff = ci1 - t_curr
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local vel = taylor_approx(vt, deriv_order, diff, dv, d2v, n)
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local idx1 = mr + 2 * (j - 2) + 2
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local idx2 = mr + 2 * (j - 2) + 3
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local temp1 = -dt * C.RECF[idx1]
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local temp3 = -C.RECF[idx2]
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local temp2 = 1 - temp3
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for i = 0, n-1 do
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Y_j[i] = temp1 * vel[i] + temp2 * Y_j_1[i] + temp3 * Y_j_2[i]
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end
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for i = 0, n-1 do Y_j_2[i] = Y_j_1[i]; Y_j_1[i] = Y_j[i] end
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ci1 = temp1 + temp2 * ci1 + temp3 * ci1 -- simplified
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end
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end
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-- ROCK4 finishing procedure (4 stages)
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local Y_base = Y_j_1
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local fpa = C.FPA[mz]; local fpb = C.FPB[mz]
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-- F1
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local diff1 = ci1 - t_curr
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local F1 = taylor_approx(vt, deriv_order, diff1, dv, d2v, n)
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local fpa0 = -dt * fpa[1]
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local Yf = {}
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for i = 0, n-1 do Yf[i] = Y_base[i] + fpa0 * F1[i] end
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-- F2
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local diff2 = ci1 + fpa0 - t_curr
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local F2 = taylor_approx(vt, deriv_order, diff2, dv, d2v, n)
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local fpa1 = -dt * fpa[2]; local fpa2 = -dt * fpa[3]
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for i = 0, n-1 do Yf[i] = Y_base[i] + fpa1 * F1[i] + fpa2 * F2[i] end
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-- F3
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local diff3 = ci1 + fpa1 + fpa2 - t_curr
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local F3 = taylor_approx(vt, deriv_order, diff3, dv, d2v, n)
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local fpa3 = -dt * fpa[4]; local fpa4 = -dt * fpa[5]; local fpa5 = -dt * fpa[6]
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-- F4
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local diff4 = ci1 + fpa3 + fpa4 + fpa5 - t_curr
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local F4 = taylor_approx(vt, deriv_order, diff4, dv, d2v, n)
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local fpb0 = -dt * fpb[1]; local fpb1 = -dt * fpb[2]; local fpb2 = -dt * fpb[3]; local fpb3 = -dt * fpb[4]
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local result = {}
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for i = 0, n-1 do
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result[i] = Y_base[i] + fpb0*F1[i] + fpb1*F2[i] + fpb2*F3[i] + fpb3*F4[i]
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end
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return result, not has_nan_inf(result, n)
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end
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local function update_history(vt, n, dt)
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local rec = {vt = {}, dt = dt}
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for i = 0, n-1 do rec.vt[i] = vt[i] end
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table.insert(velocity_history, rec)
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while #velocity_history > 3 do table.remove(velocity_history, 1) end
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end
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function step(xt, vt, t_curr, t_prev, n)
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local dt = t_curr - t_prev
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if step_index == 0 then
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velocity_history = {}
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for i = 0, n-1 do xt[i] = xt[i] - vt[i] * dt end
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update_history(vt, n, dt)
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return
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end
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local deriv_order, dv, d2v = compute_derivatives(vt, n)
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local s = math.max((params and params.substeps) or 10, 2)
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local success = false; local result
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while s >= 2 do
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result, success = rock4_substep(xt, vt, s, t_curr, t_prev, deriv_order, dv, d2v, n)
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if success then break end
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s = math.floor(s / 2)
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end
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if success then
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for i = 0, n-1 do xt[i] = result[i] end
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else
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for i = 0, n-1 do xt[i] = xt[i] - vt[i] * dt end
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end
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update_history(vt, n, dt)
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end
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