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-- coding: utf-8 --
""" Created on Fri Mar 15 15:15:44 2024 @author: """ import numpy as np from matplotlib import pyplot as plt import math
u'=0.5(x-u)
i-) Euler Yöntemi; h= 0.25 ve h=0.1; 0<=x<=
u(0)=
u(x+h)=u(x)+u'(x)*h
h=0.25 için
h1=0. x= np.arange(0,1.00001,h1) u = np.zeros(len(x)) u[0]= for i in range(0, len(x) - 1): u[i + 1] = u[i] + h10.5(x[i]-u[i]) print("") print('_' * 30) print("") print("EULER YÖNTEMİ") print("") print("") print("h=0.25 için") print("") for i in range(len(u)): print("u(",x[i],")=",u[i]) print("")
print('_' * 30) print("") plt.plot(x, u,'g-') plt.grid plt.xlabel('x values') plt.ylabel('u values') plt.title('EULER YÖNTEMİ-h=0.25') plt.tight_layout() plt.show()
h=0.1 için
h2=0. x1= np.arange(0,1.00001,h2) u1 = np.zeros(len(x1)) u1[0]= for i in range(0, len(x1) - 1): u1[i + 1] = u1[i] + h20.5(x1[i]-u1[i]) print("") print('' * 30) print("") print("EULER YÖNTEMİ") print("") print("") print("h=0.1 için") print("") for i in range(len(u1)): print("u(",round(x1[i],2),")=",u1[i]) print("") print('' * 30) print("") plt.plot(x1, u1,'g-') plt.grid plt.xlabel('x values')
print("h=0.25 için") print("") for i in range(len(u3)): print("u(",x[i],")=",u3[i]) print("") print('_' * 30) print("") plt.plot(x, u3,'g-') plt.grid plt.xlabel('x values') plt.ylabel('u values') plt.title('MODİFİYE EULER YÖNTEMİ-h=0.25') plt.tight_layout() plt.show()
h=0.1 için
u4 = np.zeros(len(x1)) u4[0]= k_1=np.zeros(len(x1)) k_2=np.zeros(len(x1)) k_1[0]=0.5(x1[0]-u4[0]) for i in range(0, len(x1) - 1): k_1[i]=0.5(x1[i]-u4[i]) k_2[i]=((h2+x1[i])-(u4[i]+h2k_1[i]))0. u4[i+1]=u4[i]+0.5h2(k_1[i]+k_2[i]) k_1[i+1]=k_2[i] print("") print('_' * 30) print("") print("MODİFİYE EULER YÖNTEMİ") print("") print("") print("h=0.1 için")
print("") for i in range(len(u4)): print("u(",round(x1[i],2),")=",u4[i]) print("") print('_' * 30) print("") plt.plot(x1, u4,'g-') plt.grid plt.xlabel('x values') plt.ylabel('u values') plt.title('MODİFİYE EULER YÖNTEMİ-h=0.1') plt.tight_layout() plt.show()
aynı grafikte
plt.plot(x, u3,label='h=0.25 için') plt.plot(x1, u4, label='h=0.1 için') plt.grid plt.xlabel('x values') plt.ylabel('u values') plt.title('MODİFİYE EULER YÖNTEMİ-h=0.25 ve h=0.1 için') plt.tight_layout() plt.legend() plt.show()
iii-) Dördüncü Derece Runge-Kutta Yöntemi; h= 0.25 ve h=0.
h=0.25 için
x= np.arange(0,1.00001,h1) u5 = np.zeros(len(x)) u5[0]= k11=np.zeros(len(x)) k22=np.zeros(len(x)) k33=np.zeros(len(x)) k44=np.zeros(len(x))
k2_2=np.zeros(len(x1)) k3_3=np.zeros(len(x1)) k4_4=np.zeros(len(x1)) for i in range(0, len(x1) - 1): k1_1[i]=0.5(x1[i]-u6[i]) k2_2[i]=((0.5h2+x1[i])-(u6[i]+0.5h2k1_1[i]))0. k3_3[i]=((0.5h2+x1[i])-(u6[i]+0.5h2k2_2[i]))0. k4_4[i]=0.5((x1[i]+h2)-(u6[i]+k3_3[i]h2)) u6[i+1]=u6[i]+(k1_1[i]+2k2_2[i]+2k3_3[i]+k4_4[i])h2/ print("") print('' * 30) print("") print("Dördüncü Derece Runge-Kutta Yöntemi") print("") print("") print("h=0.1 için") print("") for i in range(len(u6)): print("u(",round(x1[i],2),")=",u6[i]) print("") print('' * 30) print("") plt.plot(x1, u6,'g-') plt.grid plt.xlabel('x values') plt.ylabel('u values') plt.title('Dördüncü Derece Runge-Kutta Yöntemi-h=0.1') plt.tight_layout() plt.show()
aynı grafikte
plt.plot(x, u5,label='h=0.25 için')
plt.plot(x1, u6, label='h=0.1 için') plt.grid plt.xlabel('x values') plt.ylabel('u values') plt.title('4. Derece Runge-Kutta Yöntemi-h=0.25 ve h=0.1 için') plt.tight_layout() plt.legend() plt.show() #2.soru def dvdt(t,v,fs,g): return (-vfs-g) def rungeKutta(t0, v0, t, h,fs,g): n = (int((t - t0)/h)) v = v for i in range(1, n + 1): k1 = h * dvdt(t0,v,fs,g) k2 = h * dvdt(t0 + 0.5 * h, v + 0.5 * k1,fs,g) k3 = h * dvdt(t0 + 0.5 * h, v + 0.5 * k2,fs,g) k4 = h * dvdt(t0 + h, v + k3,fs,g) v = v + (1.0 / 6.0)(k1 + 2 * k2 + 2 * k3 + k4) t0 = t0 + h return v
İstediğin değeri gir
