61 lines
1.7 KiB
Lua
61 lines
1.7 KiB
Lua
-- gl2s.lua: Gauss-Legendre 2-stage implicit Runge-Kutta (4th order, 6 NFE)
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-- A-stable, symplectic. Fixed-point iteration solves the implicit system.
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solver = {
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name = "gl2s",
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display = "Gauss-Legendre 2s (6 NFE)",
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description = "Implicit 4th-order A-stable symplectic integrator",
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nfe = 6,
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order = 4,
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needs_model = true,
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stateful = false,
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stochastic = false,
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}
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-- Butcher tableau
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local SQRT3_6 = 0.28867513459481287
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local C1 = 0.5 - SQRT3_6 -- ≈ 0.2113
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local C2 = 0.5 + SQRT3_6 -- ≈ 0.7887
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local A11 = 0.25
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local A12 = 0.25 - SQRT3_6 -- ≈ -0.0387
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local A21 = 0.25 + SQRT3_6 -- ≈ 0.5387
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local A22 = 0.25
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local ITERATIONS = 3
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function step(xt, vt, t_curr, t_prev, n, model_fn, vt_buf)
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local dt = t_curr - t_prev
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-- Initialize k1 = k2 = vt
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local k1 = {}
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local k2 = {}
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for i = 0, n-1 do k1[i] = vt[i]; k2[i] = vt[i] end
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local xt_orig = {}
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for i = 0, n-1 do xt_orig[i] = xt[i] end
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local t1 = t_curr - C1 * dt
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local t2 = t_curr - C2 * dt
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-- Fixed-point iteration
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for iter = 1, ITERATIONS do
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-- Stage 1: x1 = xt - dt*(A11*k1 + A12*k2)
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for i = 0, n-1 do
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xt[i] = xt_orig[i] - dt * (A11 * k1[i] + A12 * k2[i])
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end
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model_fn(xt, t1)
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for i = 0, n-1 do k1[i] = vt_buf[i] end
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-- Stage 2: x2 = xt - dt*(A21*k1 + A22*k2)
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for i = 0, n-1 do
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xt[i] = xt_orig[i] - dt * (A21 * k1[i] + A22 * k2[i])
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end
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model_fn(xt, t2)
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for i = 0, n-1 do k2[i] = vt_buf[i] end
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end
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-- Final: xt = xt_orig - dt * 0.5 * (k1 + k2)
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for i = 0, n-1 do
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xt[i] = xt_orig[i] - dt * 0.5 * (k1[i] + k2[i])
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end
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end
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