def main(): start_time = datetime.now() # differential problem eq1 = lambda t,u : u[1] eq2 = lambda t,u : (u[0]**3)/6 - u[0] + 2* np.sin(2.7853*t) func1 = np.array([eq1,eq2]) y0 = np.array([0.,0.]) system1 = rhs.Rhs(func1, 0,20,y0, 1000 ) fwdeuler = euler.Explicit(system1) fet,feu = fwdeuler.solve() bwdeuler = euler.Backward(system1) bet,beu = bwdeuler.solve() sieuler = euler.SemiImplicit(system1) siet,sieu = sieuler.solve() #Impeuler = euler.Implicit(system1) #iet,ieu = Impeuler.solve() midpoint = centdiff.MidPoint(system1) cdt,cdu = midpoint.solve() #leapfrog = multistep.LeapFrog(system1) #lft,lfu = leapfrog.solve() # cranknicholson = rungekutta.CrankNicholson(problem1) # cnt,cnu = cranknicholson.solve() # # am5 = adamsmethods.AdamsMoulton(problem1) # amt,amu = am5._5th.solve() # rk4 = rungekutta.RK4(system1) rkt,rku = rk4.solve() #----------------------------------------------------------------------------------------------------- end_time = datetime.now() print('Duration {}'.format(end_time - start_time)) #**{'color': 'paraview'} #fig,axs = qualityplot.Standard(**{'scheme':'vega'})(1,1,figsize=(8.5,4.5))# ,**{'scheme':'nb'}) #fig,axs = qualityplot.StandardImproved(**{'scheme':'vega'} )(1,1,figsize=(9.5,4.5))# ,**{'scheme':'nb'}) #fig,axs = qualityplot.Elsevier()(1,1,figsize=(9.5,4.5))# ,**{'scheme':'nb'}) #fig,axs = qualityplot.Elsevier(figsize=(9.5,4.5),**{'scheme':'mycolor'})(1,1)# ,**{'scheme':'nb'}) #fig,axs = qualityplot.TexMathpazo(figsize=(9.5,4.5))(1,1)# ,**{'scheme':'nb'}) #fig,axs = qualityplot.TexMathpazo(figsize=(9.5,4.5),**{'scheme':'mycolor'})(1,1)# ,**{'scheme':'nb'}) #fig,axs = qualityplot.TexMathpazoBeamer(figsize=(6.5,4.5),**{'scheme':'mycolor'})(1,1)# ,**{'scheme':'nb'}) #fig,axs = qualityplot.TexPaper()(1,1,figsize=(8.5,4.5))# ,**{'scheme':'nb'}) #fig,axs = qualityplot.Helvet()(1,1,figsize=(9.5,4.5))# ,**{'scheme':'nb'}) #fig,axs = qualityplot.HelvetBeamer()(1,1,figsize=(8.5,5.5))# ,**{'scheme':'nb'}) #fig,axs = qualityplot.Beamer()(1,1,figsize=(8.5,5.5))# ,**{'scheme':'nb'}) #fig,axs = qualityplot.Times()(1,1,figsize=(9.5,4.5))# ,**{'scheme':'nb'}) #fig,axs = qualityplot.TimesItalicDefault(figsize=(9.5,4.5))(1,1)# ,**{'scheme':'nb'}) #fig,axs = qualityplot.TimesItalicImproved()(1,1,figsize=(9.5,4.5))# ,**{'scheme':'nb'}) #fig,axs = qualityplot.TimesItalicModified()(1,1,figsize=(9.5,4.5))# ,**{'scheme':'nb'}) #fig,axs = qualityplot.SansModified(figsize=(9.5,4.5),**{'scheme':'vega'} )(1,1) #fig,axs = qualityplot.Fonts(figsize=(9.5,4.5))(1,1)# ,**{'scheme':'nb'}) #fig,axs = qualityplot.Palatino(figsize=(9.5,4.5))(1,1)# ,**{'scheme':'nb'}) fig,axs = PalatinoItalic(**{'scheme':'gg' })(1,1,figsize=(9.5,4.5))# ,**{'scheme':'nb'}) #axs.plot(x,y,label='Analitycal', marker='o',linestyle='',markersize=4.5,color='C0',alpha=0.7) #axs.plot(fet,feu,label='Exp Euler') #axs.plot(iet,ieu,label='Imp Euler') #axs.plot(siet,sieu,label='Sem.Imp Euler') #, linestyle=':') axs.plot(bet,beu,label='NR-BWDEuler') #, linestyle=':') #axs.plot(lft,lfu,label='Leap Frog') #axs.plot(cnt,cnu,label='Crank Nicholson') #axs.plot(amt,amu,label='Adams Moulton 5th') #,linestyle=':') #axs.plot(rkt,rku,label='Runge Kutta 3th') axs.plot(cdt,cdu,label='CentDiff 2nd') legend = leg = axs.legend() legend.get_frame().set_linewidth(0.7) plt.setp(legend.get_texts(), color='#555555') axs.set(xlabel = 'time' ,ylabel='y(t)') axs.set_title('dy$_2$/dt = y$^3_1$/6 - y$_1$ 2 sin(2.7853 t)',y=1.05) plt.savefig('../Results/system11.pdf') plt.show()
def main(): start_time = datetime.now() eq1 = lambda t, u: (2 - 0.5 * u[1]) * u[0] #a*(u[0]-u[0]*u[1]); eq2 = lambda t, u: (-1 + 0.5 * u[0]) * u[1] #-c*(u[1]-u[0]*u[1]); func1 = np.array([eq1, eq2]) y0 = np.array([6., 2.]) system1 = rhs.Rhs(func1, 0, 15, y0, 1200) fwdeuler = euler.Explicit(system1) fet, feu = fwdeuler.solve() bwdeuler = euler.Backward(system1) bet, beu = bwdeuler.solve() sieuler = euler.SemiImplicit(system1) siet, sieu = sieuler.solve() Impeuler = euler.Implicit(system1) iet, ieu = Impeuler.solve() midpoint = centdiff.MidPoint(system1) cdt, cdu = midpoint.solve() #leapfrog = multistep.LeapFrog(system1, 'lf1.dat') #lft,lfu = leapfrog.solve() # cranknicholson = rungekutta.CrankNicholson(problem1 , 'cn1.dat') # cnt,cnu = cranknicholson.solve() # # am5 = adamsmethods.AdamsMoulton(problem1, 'AM5_1.dat') # amt,amu = am5._5th.solve() # rk3 = rungekutta.RK3(system1) rkt, rku = rk3.solve() #----------------------------------------------------------------------------------------------------- end_time = datetime.now() print('Duration {}'.format(end_time - start_time)) #**{'color': 'paraview'} #fig,axs = Standard(**{'scheme':'vega'})(1,1,figsize=(8.5,4.5))# ,**{'scheme':'nb'}) #fig,axs = StandardImproved(**{'scheme':'vega'} )(1,1,figsize=(9.5,4.5))# ,**{'scheme':'nb'}) #fig,axs = Elsevier()(1,1,figsize=(9.5,4.5))# ,**{'scheme':'nb'}) #fig,axs = Elsevier(figsize=(9.5,4.5),**{'scheme':'mycolor'})(1,1)# ,**{'scheme':'nb'}) #fig,axs = TexMathpazo(figsize=(9.5,4.5))(1,1)# ,**{'scheme':'nb'}) #fig,axs = TexMathpazo(figsize=(9.5,4.5),**{'scheme':'mycolor'})(1,1)# ,**{'scheme':'nb'}) #fig,axs = TexMathpazoBeamer(figsize=(6.5,4.5),**{'scheme':'mycolor'})(1,1)# ,**{'scheme':'nb'}) #fig,axs = TexPaper()(1,1,figsize=(8.5,4.5))# ,**{'scheme':'nb'}) #fig,axs = Helvet()(1,1,figsize=(9.5,4.5))# ,**{'scheme':'nb'}) #fig,axs = HelvetBeamer()(1,1,figsize=(8.5,5.5))# ,**{'scheme':'nb'}) #fig,axs = Beamer()(1,1,figsize=(8.5,5.5))# ,**{'scheme':'nb'}) #fig,axs = Times()(1,1,figsize=(9.5,4.5))# ,**{'scheme':'nb'}) #fig,axs = TimesItalicDefault(figsize=(9.5,4.5))(1,1)# ,**{'scheme':'nb'}) #fig,axs = TimesItalicImproved()(1,1,figsize=(9.5,4.5))# ,**{'scheme':'nb'}) #fig,axs = TimesItalicModified()(1,1,figsize=(9.5,4.5))# ,**{'scheme':'nb'}) #fig,axs = SansModified(figsize=(9.5,4.5),**{'scheme':'vega'} )(1,1) fig, axs = Fonts()(1, 1, figsize=(12.5, 4.5)) # ,**{'scheme':'nb'}) #fig,axs = Palatino(figsize=(9.5,4.5))(1,1)# ,**{'scheme':'nb'}) #fig,axs = PalatinoItalic()(1,1)# ,**{'scheme':'nb'}) #axs.plot(x,y,label='Analitycal', marker='o',linestyle='',markersize=4.5,color='C0',alpha=0.7) axs.plot(fet, feu, label='Exp Euler') #axs.plot(iet,ieu,label='Imp Euler') #axs.plot(siet,sieu,label='Sem.Imp Euler') #, linestyle=':') axs.plot(bet, beu, label='NR-BWDEuler') #, linestyle=':') #axs.plot(lft,lfu,label='Leap Frog') #axs.plot(cnt,cnu,label='Crank Nicholson') #axs.plot(amt,amu,label='Adams Moulton 5th') #,linestyle=':') #axs.plot(rkt,rku,label='Runge Kutta 3th') axs.plot(cdt, cdu, label='CentDiff 2nd') chartBox = axs.get_position() legend = leg = axs.legend() legend.get_frame().set_linewidth(0.7) axs.set_position( [chartBox.x0, chartBox.y0, chartBox.width * 0.8, chartBox.height]) plt.setp(legend.get_texts(), color='#2E3436') plt.legend(bbox_to_anchor=(1.03, 0.75), loc=2, borderaxespad=0.) #legend = leg = axs.legend() #legend.get_frame().set_linewidth(0.7) #plt.setp(legend.get_texts(), color='#2E3436') axs.set(xlabel='time', ylabel='y(t)') axs.set_title( 'dy$_1$/dt= -4 (y$_1$ - y$_1$y$_2$) ; dy$_2$/dt = -1(y$_2$ - y$_1$y$_2$)', y=1.05) plt.savefig('ODE/Results/system06.pdf') plt.show()
def main(): start_time = datetime.now() a = 4 c = 1 #y1' = (2-.5*y2)*y1 #y2' = (-1+.5*y1)*y2 #Given initial conditions #The initial rabbit population is 6, the initial fox population is 2: #y1(0) = 6 #y2(0) = 2 # differential problem PREY-PREDATOR eq1 = lambda t, u: (2 - 0.5 * u[1]) * u[0] #a*(u[0]-u[0]*u[1]); eq2 = lambda t, u: (-1 + 0.5 * u[0]) * u[1] #-c*(u[1]-u[0]*u[1]); func1 = np.array([eq1, eq2]) y0 = np.array([6., 2.]) system1 = Rhs(func1, 0, 15, y0, 1200) fwdeuler = euler.Explicit(system1) fet, feu = fwdeuler.solve() bwdeuler = euler.Backward(system1) bet, beu = bwdeuler.solve() sieuler = euler.SemiImplicit(system1) siet, sieu = sieuler.solve() Impeuler = euler.Implicit(system1) iet, ieu = Impeuler.solve() midpoint = centdiff.MidPoint(system1) cdt, cdu = midpoint.solve() #leapfrog = multistep.LeapFrog(system1, 'lf1.dat') #lft,lfu = leapfrog.solve() # cranknicholson = rungekutta.CrankNicholson(problem1 , 'cn1.dat') # cnt,cnu = cranknicholson.solve() # # am5 = adamsmethods.AdamsMoulton(problem1, 'AM5_1.dat') # amt,amu = am5._5th.solve() # # rk3 = rungekutta.RK3(system1,'s1RK4.dat') # rkt,rku = rk3.solve() # # t0 = -10. # tf = 10. # u0 = y0 # dt = 20/100 # t,u = t0,u0 # # with open('BWEuler_p1.dat', 'w') as f: # while True: # f.write('%10.4f %14.10f \n' %(t, u[0]) ) # u = euler.Backward.step(func1,t,u,dt) # t += dt # if t > tf: # break # # bet = np.genfromtxt('BWEuler_p1.dat',usecols=(0,)) # beu = np.genfromtxt('BWEuler_p1.dat',usecols=(1,)) # # t0 = -10. # tf = 10. # u0 = y0 # dt = 20/200 # t,u = t0,u0 # # with open('ImpEuler_p1.dat', 'w') as f: # while True: # f.write('%10.4f %14.10f \n' %(t, u[0]) ) # u = euler.Implicit.step(func1,t,u,dt) # t += dt # if t > tf: # break # # bt = np.genfromtxt('ImpEuler_p1.dat',usecols=(0,)) # bu = np.genfromtxt('ImpEuler_p1.dat',usecols=(1,)) # # t0 = -10. # tf = 10. # u0 = y0 # dt = 20/400 # t,u = t0,u0 # with open('SIEuler_p1.dat', 'w') as f: # while True: # f.write('%10.4f %14.10f \n' %(t, u[0]) ) # u = euler.SemiImplicit.step(func1,t,u,dt) # t += dt # if t > tf: # break # # siet = np.genfromtxt('SIEuler_p1.dat',usecols=(0,)) # sieu = np.genfromtxt('SIEuler_p1.dat',usecols=(1,)) # # t0 = -10. # tf = 10. # u0 = y0 # dt = 20/2000 # t,u = t0,u0 # with open('AdamsMoulton5_p1.dat', 'w') as f: # while True: # f.write('%f %f \n' %(t, u[0]) ) # u = adamsmethods.AdamsMoulton._5th.step(func1,t,u,dt) # t += dt # if t > tf: # break # # amt = np.genfromtxt('AdamsMoulton5_p1.dat',usecols=(0,)) # amu = np.genfromtxt('AdamsMoulton5_p1.dat',usecols=(1,)) # : a*(u[0]-u[0]*u[1]); # eq2 = lambda t,u : -c*(u[1]-u[0]*u[1]); #----------------------------------------------------------------------------------------------------- end_time = datetime.now() print('Duration {}'.format(end_time - start_time)) #**{'color': 'paraview'} ############################################################################################## #fig,axs = qualityplot.Palatino(figsize=(9.5,4.5),**{'scheme':'vega'})(1,1)# ,**{'scheme':'nb'}) # fig,axs = qualityplot.Elsevier(**{'scheme':'nb','grid.linestyle':'-','grid.dashes':(5,5)})(1,1,figsize=(9.5,4.5))# , #fig,axs = qualityplot.Elsevier(**{'scheme':'nb','grid.linestyle':'-','grid.dashes':(5,5)})(1,1,figsize=(9.5,4.5))# #fig,axs = qualityplot.StandardImproved(**{'scheme':'vega','grid.dashes':(5,5), 'linestyle':'ls1'})(1,1,figsize=(9.5,4.5))# # fig,axs = qualityplot.StandardImproved(**{'scheme':'vega','grid.dashes':(5,5), 'linestyle':'paper'})(1,1,figsize=(9.5,4.5))# #fig,axs = qualityplot.TexMathpazo(**{'scheme':'vega','grid.dashes':(5,5), 'linestyle':'paper'})(1,1,figsize=(9.5,4.5))# #fig,axs = qualityplot.TexMathpazoBeamer(**{'scheme':'nb','grid.dashes':(5,5), 'linestyle':'paper'})(1,1,figsize=(9.5,4.5))# #fig,axs = qualityplot.Beamer(**{'scheme':'nb','grid.dashes':(5,5), 'linestyle':'paper'})(1,1,figsize=(9.5,4.5))# #fig,axs = qualityplot.TexPaper(**{'scheme':'nb', 'linestyle':'paper'})(1,1,figsize=(9.5,4.5))# #fig,axs = qualityplot.Helvet(**{'scheme':'nb', 'linestyle':'paper'})(1,1,figsize=(9.5,4.5))# #fig,axs = qualityplot.HelvetBeamer(**{'linestyle':'paper'})(1,1) #,figsize=(9.5,4.5))# #fig,axs = qualityplot.Times(**{'linestyle':'paper'})(1,1,figsize=(12.5,4.5))# ,**{'scheme':'nb'}) #fig,axs = qualityplot.TimesItalic(**{'linestyle':'paper'})(1,1,figsize=(9.5,4.5))# #fig,axs = qualityplot.TimesItalic(**{'linestyle':'paper'})(1,1,figsize=(9.5,4.5))# fig, axs = PalatinoItalic()(1, 1, (12.0, 4.0)) # #fig,axs = qualityplot.SansItalic()(1,1,(12.0,4.0))# # fig,axs = PalatinoItalicDark()(1,1)# #fig,axs = qualityplot.PalatinoItalicDark()(1,1)# #axs.plot(x,y,label='Analitycal', marker='o',linestyle='',markersize=4.5,color='C0',alpha=0.7) axs.plot(fet, feu, label='Exp Euler') #axs.plot(iet,ieu,label='Imp Euler') #axs.plot(siet,sieu,label='Sem.Imp Euler') #, linestyle=':') axs.plot(bet, beu, label='NR-BWDEuler') #, linestyle=':') #axs.plot(lft,lfu,label='Leap Frog') #axs.plot(cnt,cnu,label='Crank Nicholson') #axs.plot(amt,amu,label='Adams Moulton 5th') #,linestyle=':') #axs.plot(rkt,rku,label='Runge Kutta 3th') axs.plot(cdt, cdu, label='CentDiff 2nd') chartBox = axs.get_position() legend = leg = axs.legend() legend.get_frame().set_linewidth(0.7) axs.set_position( [chartBox.x0, chartBox.y0, chartBox.width * 0.8, chartBox.height]) plt.setp(legend.get_texts(), color='#2E3436') plt.legend(bbox_to_anchor=(1.03, 0.75), loc=2, borderaxespad=0.) #legend = leg = axs.legend() #legend.get_frame().set_linewidth(0.7) #plt.setp(legend.get_texts(), color='#2E3436') axs.set(xlabel='time', ylabel='y(t)') axs.set_title( 'dy$_1$/dt= -4 (y$_1$ - y$_1$y$_2$) ; dy$_2$/dt = -1(y$_2$ - y$_1$y$_2$)', y=1.05) plt.savefig('../Results/systemPrayPredator_1.pdf') plt.show()