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()