CoCalc Public Files7 / 7_1.sagewsOpen with one click!
Author: Georgy Lazarev
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Compute Environment: Ubuntu 18.04 (Deprecated)
var('t y') f(t,y)=y/(t+1)+(t+1)*exp(t) y_0=1 t0=0 T=1 h=0.1 n=(T-t0)/h n def eyler(h): n=abs(T-t0)/h y=y_0 e=[] for i in range(n): y=(y+h*f(t0+i*h,y)).n() e.append(y) return e eyler(0.1) def rkfixed(h): n=(T-t0)/h y=y_0 t=t0 a=[] for i in range(n): k1=f(t,y)*h k2=f(t+h/2,y+k1/2)*h k3=f(t+h/2,y+k2/2)*h k4=f(t+h,y+k3)*h y=(y+(k1+2*k2+2*k3+k4)/6).n() a.append(y) t=t+h return a t=t0 th=[] th2=[] for i in range(n): t=t+0.1 th.append(exp(t)*(t+1)) t=t0 for i in range(n): t=t+0.2 th2.append(exp(t)*(t+1)) #plot(exp(t)*(t+1),(t,0,1)) e=copy(eyler(0.1)) e2=copy(eyler(0.2)) r=copy(rkfixed(0.1)) r2=copy(rkfixed(0.2)) th th2 e e2 print("Погрешность метода Элера, первый способ") c=[] for i in range(len(e)): c.append(abs(e[i]-th[i])) max(c) print("Погрешность метода Рунге-Кутты, первый способ") d=[] for i in range(n): d.append(abs(r[i]-th[i])) max(d) print("Погрешность метода Эйлера по правилу Рунге") p=1 f=[] n/2 for i in range(n/2): f.append(abs((e[2*i]-e2[i])/(2^p-1))) f eyler(0.1) print("Погрешность метода Рунге_Кутты по правилу Рунге") g=[] p=4 for i in range(n/2): g.append(abs(r[2*i]-r2[i])/(2^p-1)) g def theor(h): th=[] n=(abs(T-t0))/h for i in range(n): t=t+h th.append(exp(t)*(t+1)) return th def eyler_err(h): e=copy(eyler(h)) c=[] th=copy(theor(h)) for i in range(len(e)): c.append(abs(e[i]-th[i])) return max(c) eyler(0.1) h=0.1 k=0 #while (k<10): #k+=1 #k #eyler_err(h) #a #if abs(a)<rker: #break #else: #h=h/2
(t, y) 10.0000000000000 [1.20000000000000, 1.43065971007923, 1.69644968356505, 2.00242745805494, 2.35431344844293, 2.75857586894414, 3.22252586881563, 3.75442417431006, 4.36360066223371, 5.06058844610267] [1.21568800988321, 1.46568330979220, 1.75481644984880, 2.08855457669778, 2.47308190605019, 2.91539008062481, 3.42337960269981, 4.00597367128644, 4.67324591119820, 5.43656365691809] [1.46568330979220, 2.08855457669778, 2.91539008062481, 4.00597367128644, 5.43656365691809, 7.30425723002040, 9.73247992042722, 12.8778843034273, 16.9390129003562, 22.1671682967919] [1.20000000000000, 1.43065971007923, 1.69644968356505, 2.00242745805494, 2.35431344844293, 2.75857586894414, 3.22252586881563, 3.75442417431006, 4.36360066223371, 5.06058844610267] [1.40000000000000, 1.92646999529177, 2.61939090995873, 3.52989278982853, 4.72329783406677] Погрешность метода Элера, первый способ 0.375975210815418 Погрешность метода Рунге-Кутты, первый способ 2.82251300287584e-6 Погрешность метода Эйлера по правилу Рунге 5.00000000000000 [0.200000000000000, 0.230020311726721, 0.265077461515800, 0.307366921012899, 0.359697171833058]
Error in lines 68-68 Traceback (most recent call last): File "/projects/sage/sage-6.10/local/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 905, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "", line 1, in <module> File "", line 6, in eyler TypeError: 'list' object is not callable