Re: [微積] 請問一下離散的微分方程的解法

看板Math作者Frobenius (▽．(▽×▽φ)=0)時間15年前 (2011/04/03 15:12)推噓1(1推 0噓 10→)

留言11則, 2人參與討論串1/2 (看更多)

※ 引述《igawa (井穿腸 (3A))》之銘言： : 就是我有一組數據 : du/dt = 10 @ t=0 : du/dt = 22 @ t=1 : du/dt = 73 @ t=2 : du/dt = 68 @ t=3 : du/dt = 17 @ t=4 : du/dt = 11 @ t=5 : . : . : . : 想請問版上先進,可以用哪些方法,把u(t)這個函數解出來 : 謝謝~~! 定義 du/dt = v[t] RSolve[{v[0] == 10, v[1] == 22, v[2] == 73, v[3] == 68, v[4] == 17, v[5] == 11}, v[t], t] RSolve::deqx: Supplied equations are not difference equations of the given functions. >> Solve[{a 0^6 + b 0^5 + c 0^4 + d 0^3 + e 0^2 + f 0 + g == 10, a 1^6 + b 1^5 + c 1^4 + d 1^3 + e 1^2 + f 1 + g == 22, a 2^6 + b 2^5 + c 2^4 + d 2^3 + e 2^2 + f 2 + g == 73, a 3^6 + b 3^5 + c 3^4 + d 3^3 + e 3^2 + f 3 + g == 68, a 4^6 + b 4^5 + c 4^4 + d 4^3 + e 4^2 + f 4 + g == 17, a 5^6 + b 5^5 + c 5^4 + d 5^3 + e 5^2 + f 5 + g == 11}, {a, b, c, d, e, f, g}] Solve::svars: Equations may not give solutions for all "solve" variables. >> {{a -> -(4213/7200) - f/120, b -> 4117/480 + f/8, c -> -(62441/1440) - (17 f)/24, d -> 7927/96 + (15 f)/8, e -> -(126731/3600) - (137 f)/60, g -> 10}} v[t_] = (-(4213/7200) - f/120) t^6 + (4117/480 + f/ 8) t^5 + (-(62441/1440) - (17 f)/24) t^4 + (7927/96 + (15 f)/ 8) t^3 + (-(126731/3600) - (137 f)/60) t^2 + f t + 10; Table[v[t], {t, 0, 5, 1}] // FullSimplify {10, 22, 73, 68, 17, 11} u[t_] = 1/7 (-(4213/7200) - f/120) t^7 + 1/6 (4117/480 + f/8) t^6 + 1/5 (-(62441/1440) - (17 f)/24) t^5 + 1/4 (7927/96 + (15 f)/8) t^4 + 1/3 (-(126731/3600) - (137 f)/60) t^3 + 1/2 f t^2 + 10 t + h Table[u[t], {t, 0, 5, 1}] // FullSimplify {h, (7005059 + 51780 f)/604800 + h, 2256301/37800 + (37 f)/630 + h, 3073097/22400 + (87 f)/1120 + h, 845302/4725 + (16 f)/315 + h, (5 (917759 + 660 f))/24192 + h} 4213 f 7 4117 f 6 62441 17 f 5 (-(----) - ---) t (---- + -) t (-(-----) - ----) t 7200 120 480 8 1440 24 u[t] = ------------------ + ------------- + -------------------- 7 6 5 7927 15 f 4 126731 137 f 3 (---- + ----) t (-(------) - -----) t 2 96 8 3600 60 f t + ---------------- + ---------------------- + ---- + 10 t + h 4 3 2 4213 f 6 4117 f 5 62441 17 f 4 u'[t] = v[t] = (-(----) - ---) t + (---- + -) t + (-(-----) - ----) t 7200 120 480 8 1440 24 7927 15 f 3 126731 137 f 2 + (---- + ----) t + (-(------) - -----) t + f t + 10 96 8 3600 60 4213 f 5 4117 f 4 u''[t] = v'[t] = 6 (-(----) - ---) t + 5 (---- + -) t 7200 120 480 8 62441 17 f 3 7927 15 f 2 + 4 (-(-----) - ----) t + 3 (---- + ----) t 1440 24 96 8 126731 137 f + 2 (-(------) - -----) t + f 3600 60 u[0] = h ; u'[0] = v[0] = 10 ; u''[0] = v'[0] = f 7005059 + 51780 f 1081 f u[1] = ----------------- + h ; u'[1] = v[1] = 22 ; u''[1] = v'[1] = ---- - - 604800 25 5 2256301 37 f 7261 f u[2] = ------- + ---- + h ; u'[2] = v[2] = 73 ; u''[2] = v'[2] = ---- + -- 37800 630 200 10 3073097 87 f 26543 f u[3] = ------- + ---- + h ; u'[3] = v[3] = 68 ; u''[3] = v'[3] = - ----- - -- 22400 1120 600 10 845302 16 f 2638 f u[4] = ------ + ---- + h ; u'[4] = v[4] = 17 ; u''[4] = v'[4] = - ---- + - 4725 315 75 5 4588795 + 3300 f 119 u[5] = ---------------- + h ; u'[5] = v[5] = 11 ; u''[5] = v'[5] = - --- - f 24192 15 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 118.161.243.220

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