Runge-Kutta fifth order adaptive step

true RK5adapt Runge-Kutta fifth order adaptive step Runge-Kutta fifth order method vith adaptive step for solving system of first order ODE - initial value problem 2 decimal true

Метод Рунге-Кутта пятого порядка с автоматическим выбором шага

Metode Runge-Kutta orde lima dengan langkah adaptif

Fifth-order Runge–Kutta method with adaptive step

t1 T h x ε 2 f RK5adapt t1-Start Point of indep.var. T-Segment length h-step value x-vector of initial values dep.var ε - precission j t1 h + ← j T t1 + h + ≤ j j h + ← tx x x cols col ← k1 h 3 / j tx f eval * ← k2 h 3 / j h 3 / + tx k1 + f eval * ← k3 h 3 / j h 3 / + tx k1 k2 + 2 / + f eval * ← k4 h 3 / j h 2 / + tx 3 k1 * 9 k3 * + 8 / + f eval * ← k5 h 3 / j h + tx 3 k1 * 9 k3 * - 2 / + 6 k4 * + f eval * ← δ k1 92 / k3 * - 4 k4 * + 12 / k5 * - ← δ min abs 5 ε * ≤ (δ max abs 5 ε * ≤ (& x x tx 12 / k1 4 k4 * + k5 + (* + augment ← steps 1 x cols el j ← h h 2 * ← 31 line j j h - ← h h 2 / ← 21 line if 81 line for result steps x stack transpose ← 71 line ←