Numeric Analysis Engineering, Assignments of Mathematical Methods for Numerical Analysis and Optimization

Download Numeric Analysis Engineering and more Assignments Mathematical Methods for Numerical Analysis and Optimization in PDF only on Docsity! # -*- 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<=1 # u(0)=1 # u(x+h)=u(x)+u'(x)*h # h=0.25 için h1=0.25 x= np.arange(0,1.00001,h1) u = np.zeros(len(x)) u[0]=1 for i in range(0, len(x) - 1): u[i + 1] = u[i] + h1*0.5*(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=0.1 x1= np.arange(0,1.00001,h2) u1 = np.zeros(len(x1)) u1[0]=1 for i in range(0, len(x1) - 1): u1[i + 1] = u1[i] + h2*0.5*(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("") 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=0.1 # h=0.25 için x= np.arange(0,1.00001,h1) u5 = np.zeros(len(x)) u5[0]=1 k11=np.zeros(len(x)) k22=np.zeros(len(x)) k33=np.zeros(len(x)) k44=np.zeros(len(x)) for i in range(0, len(x) - 1): k11[i]=0.5*(x[i]-u5[i]) k22[i]=((0.5*h1+x[i])-(u5[i]+0.5*h1*k11[i]))*0.5 k33[i]=((0.5*h1+x[i])-(u5[i]+0.5*h1*k22[i]))*0.5 k44[i]=0.5*((x[i]+h1)-(u5[i]+k33[i]*h1)) u5[i+1]=u5[i]+(k11[i]+2*k22[i]+2*k33[i]+k44[i])*h1/6 print("") print('_' * 30) print("") print("Dördüncü Derece Runge-Kutta Yöntemi") print("") print("") print("h=0.25 için") print("") for i in range(len(u5)): print("u(",x[i],")=",u5[i]) print("") print('_' * 30) print("") plt.plot(x, u5,'g-') plt.grid plt.xlabel('x values') plt.ylabel('u values') plt.title('Dördüncü Derece Runge-Kutta Yöntemi-h=0.25') plt.tight_layout() plt.show() # h=0.1 için x1= np.arange(0,1.00001,h2) u6 = np.zeros(len(x1)) u6[0]=1 k1_1=np.zeros(len(x1)) 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]=((0.5*h2+x1[i])-(u6[i]+0.5*h2*k1_1[i]))*0.5 k3_3[i]=((0.5*h2+x1[i])-(u6[i]+0.5*h2*k2_2[i]))*0.5 k4_4[i]=0.5*((x1[i]+h2)-(u6[i]+k3_3[i]*h2)) u6[i+1]=u6[i]+(k1_1[i]+2*k2_2[i]+2*k3_3[i]+k4_4[i])*h2/6 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')