标题: 四阶RK法求解常微分方程 [打印本页] 作者: 2744557306 时间: 2023-12-31 17:32 标题: 四阶RK法求解常微分方程 这段MATLAB代码实现了四阶Runge-Kutta（RK）方法来求解常微分方程（ODE）。以下是代码的主要解释：+ @4 S2 Q, c7 E" w! c/ w
function y = RK(a, b, N, af) $ n9 p8 i8 ?/ `& C h = (b - a) / N; 0 K' b$ j B/ P1 T( Z% o7 j x(1) = a; " p2 _. b9 ` ~# m7 J9 S" @0 M2 x y(1) = af; . Y8 ]3 N! T7 j) p/ j jqj(1) = af; 8 y; }% Q8 q+ `3 V n/ i: S2 m # E: ^* [: I q @ for i = 2:N+1 p2 K2 R3 B6 t* w2 d K1 = f(x(i-1), y(i-1)); ( e+ o9 C* S! R' X, } K2 = f(x(i-1) + h/2, y(i-1) + h*K1/2); $ \ y) W6 J8 x, p7 U K3 = f(x(i-1) + h/2, y(i-1) + h*K2/2);. B; q" i. ^' X
K4 = f(x(i-1) + h, y(i-1) + h*K3);& K9 b' \" R8 U2 n
7 }% K: V8 f H5 M y(i) = y(i-1) + (K1 + 2*K2 + 2*K3 + K4) / 6;9 u& S$ s. @! P* V X6 l" C
x(i) = x(i-1) + (i-1) * h; + V& ] C% M( b. p1 k+ T jqj(i) = x(i) + exp(-x(i));9 h" \6 p. j1 p- F9 m
end - N0 u2 a. [5 c$ A" p. c ( z! X9 n" N. ]. C [x', y', jqj']9 P9 f* Z2 {; i: G7 a# |# k
er = norm(y - jqj, 2) / norm(y); a) v/ c) a+ }2 ]: b, P6 Y8 Z
) U' {" Y: W. J+ ?% @* b- Y: U( ] plot(x', y', 'r', x', jqj', 'g'); / l4 `9 r, _8 k% B legend('RK法', '精确解'); ~. z. R! A- W/ h( l: \' o; Z
end7 x4 E$ O$ L, c1 }
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这是代码的简要说明：% e0 k9 f0 B. G6 R8 O