def main():
start_time = datetime.now()
# differential problem
eq1 = lambda t, u: u[1]
eq2 = lambda t, u: u[2]
eq3 = lambda t, u: u[3]
eq4 = lambda t, u: -8 * u[0] + np.sin(t) * u[1] - 3 * u[3] + t**2
func1 = np.array([eq1, eq2, eq3, eq4])
y0 = np.array([1., 2., 3., 4])
system1 = rhs.Rhs(func1, 0, 4, y0, 100)
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()
leapfrog = multistep.LeapFrog(system1)
lft, lfu = leapfrog.solve()
#-----------------------------------------------------------------------------------------------------
end_time = datetime.now()
print('Duration {}'.format(end_time - start_time))
#**{'color': 'paraview'}
fig, axs = PalatinoItalic()(1, 1, figsize=(9.5, 4.5))
#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 4th',linestyle=':')
legend = leg = axs.legend()
legend.get_frame().set_linewidth(1.2)
plt.setp(legend.get_texts(), color='#555555')
axs.set(xlabel='time', ylabel='y(t)')
axs.set_title(
'dy$_1$/dt=y$_2$; dy$_2$/dt=y$_3$; dy$_3$/dt=y$_4$ ; dy$_4$/dt=-8y$_1$+sin(t)y$_2$-3y$_4$',
y=1.05)
plt.savefig('ODE/Results/system01.pdf')
plt.show()
def main():
start_time = datetime.now()
# differential problem
eq1 = lambda t, u: u[1]
eq2 = lambda t, u: -1 / 2. * u[0] + 5 / 2. * u[1]
func1 = np.array([eq1, eq2])
y0 = np.array([6., -1.])
system1 = rhs.Rhs(func1, 3, 5, y0, 50)
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()
leapfrog = multistep.LeapFrog(system1)
lft, lfu = leapfrog.solve()
#--------------------------------------------------------------------------------------------
end_time = datetime.now()
print('Duration {}'.format(end_time - start_time))
#**{'color': 'paraview'}
fig, axs = PalatinoItalic()(1, 1, figsize=(9.5, 4.5))
#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[:,3],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 4th',linestyle=':')
legend = leg = axs.legend()
legend.get_frame().set_linewidth(1.2)
plt.setp(legend.get_texts(), color='#555555')
axs.set(xlabel='time', ylabel='y(t)')
axs.set_title('2 y" - 5 y\' + y', y=1.05)
plt.ylim(-300, 50)
plt.savefig('ODE/Results/system05.pdf')
plt.show()
def main():
start_time = datetime.now()
###--- differential problem ---###
eq1 = lambda t, u: u[1]
eq2 = lambda t, u: u[2]
eq3 = lambda t, u: 4 * u[0] - 3 * u[1] + 2 * u[2]
func1 = np.array([eq1, eq2, eq3])
y0 = np.array([0.1, 0.5, 0.1])
system1 = rhs.Rhs(func1, 0, 2, y0, 100)
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()
leapfrog = multistep.LeapFrog(system1)
lft, lfu = leapfrog.solve()
#----------------------------------------------------------------------------------------------
end_time = datetime.now()
print('Duration {}'.format(end_time - start_time))
fig, axs = PalatinoItalic()(1, 1, figsize=(9.5, 4.5))
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[:,3],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 4th',linestyle=':')
legend = leg = axs.legend()
legend.get_frame().set_linewidth(1.2)
plt.setp(legend.get_texts(), color='#555555')
axs.set(xlabel='time', ylabel='y(t)')
axs.set_title(
'dy$_1$/dt = y$_2$ ; dy$_2$/dt = y$_3$ ; dy$_3$/dt = 4y$_1$+3y$_2$+2y$_3$ ',
y=1.05)
plt.savefig('ODE/Results/system04.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;
# differential problem
eq1 = lambda t,u : a*(u[0]-u[0]*u[1]);
eq2 = lambda t,u : -c*(u[1]-u[0]*u[1]);
func1 = np.array([eq1,eq2])
y0 = np.array([2.,1.])
system1 = rhs.Rhs(func1, 0,10,y0,500 )
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()
leapfrog = multistep.LeapFrog(system1)
lft,lfu = leapfrog.solve()
rk3 = rungekutta.RK3(system1)
rkt,rku = rk3.solve()
fig,axs = SansItalic()(1,1,figsize=(9.5,4.5))# ,**{'scheme':'nb'})
#----------------------------------------------------------------------------------------------
end_time = datetime.now()
print('Duration {}'.format(end_time - start_time))
#**{'color': 'paraview'}
#fig,axs = Standard(figsize=(9.5,4.5))(1,1)# ,**{'scheme':'nb'})
#fig,axs = StandardImproved(figsize=(9.5,4.5))(1,1)# ,**{'scheme':'nb'})
#fig,axs = Elsevier(figsize=(9.5,4.5))(1,1)# ,**{'scheme':'nb'})
#fig,axs = TexMathpazo(figsize=(9.5,4.5))(1,1)# ,**{'scheme':'nb'})
#fig,axs = TexMathpazoBeamer(figsize=(9.5,4.5))(1,1)# ,**{'scheme':'nb'})
#fig,axs = Beamer(figsize=(6.5,4.5))(1,1)# ,**{'scheme':'nb'})
#fig,axs = TexPaper(figsize=(9.5,4.5))(1,1)# ,**{'scheme':'nb'})
#fig,axs = Helvet(figsize=(9.5,4.5))(1,1)# ,**{'scheme':'nb'})
#fig,axs = HelvetBeamer(figsize=(9.5,4.5))(1,1)# ,**{'scheme':'nb'})
#fig,axs = Times(figsize=(9.5,4.5))(1,1)# ,**{'scheme':'nb'})
#fig,axs = TimesItalicDefault(figsize=(9.5,4.5))(1,1)# ,**{'scheme':'nb'})
#fig,axs = TimesItalicImproved(figsize=(9.5,4.5))(1,1)# ,**{'scheme':'nb'})
#fig,axs = PalatinoItalic(figsize=(9.5,4.5))(1,1)# ,**{'scheme':'nb'})
#fig,axs = Fonts(figsize=(9.5,4.5))(1,1)# ,**{'scheme':'nb'})
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',linestyle=':')
legend = leg = axs.legend()
legend.get_frame().set_linewidth(1.2)
plt.legend(loc='upper left')
#axs.plot(x,y,label='Analitycal', marker='o',linestyle='',markersize=4.5,color='C0',alpha=0.7)
plt.setp(legend.get_texts(), color='#555555')
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/system02.pdf')
plt.show()
def main():
start_time = datetime.now()
# differential problem
m = 10
k = 3
g = 0.5
eq1 = lambda t, u: u[1]
eq2 = lambda t, u: -k / m * u[0] - g / m * u[1] + np.sin(t) / m
func1 = np.array([eq1, eq2])
y0 = np.array([0.1, 0.1])
system1 = rhs.Rhs(func1, 0, 50, 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()
leapfrog = multistep.LeapFrog(system1)
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()
#
# rk4 = rungekutta.RK4(problem1,'RK4.dat')
# rkt,rku = rk4.solve()
#----------------------------------------------------------------------------------------------
end_time = datetime.now()
print('Duration {}'.format(end_time - start_time))
#**{'color': 'paraview'}
fig, axs = PalatinoItalic()(1, 1, figsize=(9.5, 4.5))
#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[:,3],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 4th',linestyle=':')
legend = leg = axs.legend()
legend.get_frame().set_linewidth(1.2)
plt.setp(legend.get_texts(), color='#555555')
axs.set(xlabel='time', ylabel='y(t)')
axs.set_title(
'dy$_1$/dt = y$_2$ ; dy$_2$/dt = -k/m y$_1$ -g/m y$_2$ + sin(t)/m ',
y=1.05)
plt.savefig('ODE/Results/system03.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()
def main():
start_time = datetime.now()
y0 = np.array([0.])
problem1 = rhs.Rhs(func0, 0.0, 2.0, y0, 30, anal01)
x, y = problem1.analiticalSolution(save=True)
#------------------------------------------------------------------------------------------------------------------------------------
#------------------------------------------------------------------------------------------------------------------------------------
#------------------------------------------------------------------------------------------------------------------------------------
bwdeuler = euler.Implicit(problem1, 'bwe.dat')
bet, beu = bwdeuler.solve()
# sieuler_p1 = euler.SemiImplicit(problem1, 'bwe.dat')
# siet,sieu = sieuler_p1.solve()
beuler = euler.Backward(problem1, 'bwe.dat')
bt, bu = beuler.solve()
ieuler = impliciteuler.BWDEuler(problem1, 'bwe.dat')
iet, ieu = ieuler.solve()
# midpoint = centdiff.MidPointSolver(problem1 , 'mp.dat')
# cdt,cdu = midpoint.solve()
#sieuler_p4 = euler.Implicit(problem1, 'bwe.dat')
#siet,sieu = bwdeuler_p4.solve()
implicitmidpoint = centdiff.ImplicitMidPoint(problem1, 'Imp_mp.dat')
impt, impu = implicitmidpoint.solve()
# impmidpoint = centdiff.ImpMidPoint(problem1 , 'Imp_mp.dat')
# it,iu = impmidpoint.solve()
cn_p2 = rungekutta.ImplicitCrankNicholson(problem1, 'cn.dat')
cnt, cnu = cn_p2.solve()
#
rk_p1 = implicitrungekutta.ImpRK2(problem1, 'rk.dat')
rkt, rku = rk_p1.solve()
#
# #fwdeuler_p1 = euler.Explicit(problem1, True, True, 'lorentz_fwe.dat')
# #fet,feu = fwdeuler_p1.solve()
#
#leapfrog_p1 = multistep.LeapFrog(problem1, 'lorentz_lf.dat')
#lft,lfu = leapfrog_p1.solve()
#
# leapfrog_p2 = euler.Explicit(problem2, 'oscillator_lf.dat')
# lf2,lf2 = leapfrog_p2.solve()
rk = implicitrungekutta.ImpRK4(problem1, 'rk.dat')
rk3t, rk3u = rk.solve()
bdf = MEBDF(problem1, 'bdf.dat')
bdft, bdfu = bdf.solve(1, 0.5)
radau = RadauIIA(problem1, 'radau.dat')
rdt, rdu = radau.solve()
radau = RadauIIA5th(problem1, 'radau.dat')
rd5t, rd5u = radau.solve()
end_time = datetime.now()
print('Duration: {}'.format(end_time - start_time))
fig, axs = qualityplot.Fonts()(
1, 1) #mkplot.PlotBase('Solution of Differential Equations','p1.pdf')
# 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(bt,bu,label='NR-BWDEuler') #, linestyle=':')
# axs.plot(bet,beu,label='Imp Euler') #, linestyle=':')
axs.plot(rdt, rdu, label='RadauIIA')
axs.plot(rd5t, rd5u, label='RadauIIA 5th')
#axs.plot(cnt,cnu,label='Implicit Crank Nicholson',linestyle='-')
#axs.plot(rkt,rku,label='Runge Kutta 4th') #,linestyle=':')
#axs.plot(am3t,am3u,label='Adams Moulton 3rd') #,linestyle=':')
#axs.plot(am4t,am4u,label='Adams Moulton 4th') #,linestyle=':')
axs.plot(bdft, bdfu, label='BDF')
# axs.plot(rkt,rku,label='Imp. Runge Kutta')
#axs.plot(impt,impu,label='Implicit Mid-Point Method',linestyle='--')
#axs.plot(iet,ieu,label='NR Implicit Euler') #,linestyle='-.')
axs.plot(rk3t, rk3u, label='Imp. RK4') #,linestyle='-.')
axs.plot(x,
y,
label='Analitical',
marker='o',
markersize='7',
linestyle='',
color='C0',
alpha=0.7) #, linestyle=':')
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$_1$/dt=-10(t-1)y$_1$', y=1.05)
plt.savefig('../Results/StiffEq2.pdf')
plt.show()
def main():
start_time = datetime.now()
y0 = np.array([2. / 3. * np.exp(2), 1])
problem1 = rhs.Rhs(func0, 0.0, 3.0, y0, 30)
#x,y = problem1.analiticalSolution(save=True)
##------------------------------------------------------------------------------------------------------------
##------------------------------------------------------------------------------------------------------------
##------------------------------------------------------------------------------------------------------------
fwdeuler_p1 = euler.Explicit(problem1, 'fwe.dat')
fet, feu = fwdeuler_p1.solve()
bwdeuler_p1 = euler.Implicit(problem1, 'bwe.dat')
bet, beu = bwdeuler_p1.solve()
# sieuler_p1 = euler.SemiImplicit(problem1, 'bwe.dat')
# siet,sieu = sieuler_p1.solve()
beuler_p1 = euler.Backward(problem1, 'bwe.dat')
bt, bu = beuler_p1.solve()
# midpoint = centdiff.MidPointSolver(problem1 , 'mp.dat')
# cdt,cdu = midpoint.solve()
#sieuler_p4 = euler.Implicit(problem1, 'bwe.dat')
#siet,sieu = bwdeuler_p4.solve()
implicitmidpoint = centdiff.ImplicitMidPoint(problem1, 'Imp_mp.dat')
impt, impu = implicitmidpoint.solve()
am5_p1 = adamsmoulton.AdamsMoulton5th(problem1, 'am5_1.dat')
#ab2_p = ab2_p1._2nd(problem1,'ab2_1.dat')
am5t, am5u = am5_p1.solve()
impcn = implicitrungekutta.ImpRK4(problem1, 'cn.dat')
rkt, rku = impcn.solve()
radau = RadauIIA(problem1, 'radIIA.dat')
radt, radu = radau.solve()
radau5 = RadauIIA5th(problem1, 'radIIA.dat')
rad5t, rad5u = radau5.solve()
# rk_p1 = rungekutta.RK4(problem1, 'rk.dat')
# rkt,rku = rk_p1.solve()
#
#rk3 = implicitrungekutta.ImpRK4(problem1, 'rk.dat')
#rk3t,rk3u = rk3.solve()
# #fwdeuler_p1 = euler.Explicit(problem1, True, True, 'lorentz_fwe.dat')
# #fet,feu = fwdeuler_p1.solve()
#
#leapfrog_p1 = multistep.LeapFrog(problem1, 'lorentz_lf.dat')
#lft,lfu = leapfrog_p1.solve()
#
# leapfrog_p2 = euler.Explicit(problem2, 'oscillator_lf.dat')
# lf2,lf2 = leapfrog_p2.solve()
#fwdeuler_p1.plot()
#ab2_p1 = euler.Implicit(problem3,True,True,filename='lorentz_bwe.dat')
#bet,beu = bwdeuler_p1.solve()
#bwdeuler_p1.plot()
end_time = datetime.now()
print('Duration: {}'.format(end_time - start_time))
fig, axs = qualityplot.Fonts()(
1, 1) #mkplot.PlotBase('Solution of Differential Equations','p1.pdf')
# 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(bt, bu, label='NR-BWDEuler') #, linestyle=':')
# axs.plot(bet,beu,label='Imp Euler') #, linestyle=':')
axs.plot(radt, radu, label='RadauIIA 3th', linewidth=3)
axs.plot(rad5t, rad5u, label='RadauIIA 5th', linewidth=3)
axs.plot(rkt, rku, label='Imp RK4', linewidth=2)
#axs.plot(am5t,am5u,label='Adams Moulton') #,linestyle=':')
#axs.plot(am3t,am3u,label='Adams Moulton 3rd') #,linestyle=':')
#axs.plot(am4t,am4u,label='Adams Moulton 4th') #,linestyle=':')
#axs.plot(cd2t,cd2u,label='Cent diff 2nd')
#axs.plot(impt,impu,label='Implicit Mid-Point Method',linestyle='-.')
#axs.plot(x,y,label='Analitical', marker='o',linestyle='',color='C0',alpha=0.7 ) #, linestyle=':')
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$_1$/dt=-10(t-1)y$_1$', y=1.05)
plt.savefig('../Results/StiffSys1.pdf')
plt.show()
def main():
start_time = datetime.now()
eq1 = lambda t, u: (2 - 0.5 * u[1]) * u[0]
eq2 = lambda t, u: (-1 + 0.5 * 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()
#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()(1, 1, figsize=(9.5, 4.5)) # ,**{'scheme':'nb'})
#fig,axs = qualityplot.StandardImproved(figsize=(9.5,4.5),**{'scheme':'ernest'})(1,1)# ,**{'scheme':'nb'})
#fig,axs = qualityplot.Elsevier(figsize=(9.5,4.5))(1,1)# ,**{'scheme':'nb'})
#fig,axs = qualityplot.TexMathpazo(figsize=(9.5,4.5))(1,1)# ,**{'scheme':'nb'})
#fig,axs = qualityplot.TexMathpazoBeamer(figsize=(6.5,4.5))(1,1)# ,**{'scheme':'nb'})
#fig,axs = qualityplot.TexPaper(figsize=(9.5,4.5))(1,1)# ,**{'scheme':'nb'})
#fig,axs = qualityplot.Beamer(figsize=(6.5,4.5))(1,1)# ,**{'scheme':'nb'})
#fig,axs = qualityplot.Helvet(figsize=(9.5,4.5))(1,1)# ,**{'scheme':'nb'})
#fig,axs = qualityplot.Times(figsize=(9.5,4.5))(1,1)# ,**{'scheme':'nb'})
#fig,axs = qualityplot.TimesItalicDefault(figsize=(9.5,4.5))(1,1,**{ 'legend.loc':'upper left'})
#fig,axs = qualityplot.TimesItalicImproved(figsize=(9.5,4.5))(1,1)# ,**{'scheme':'nb'})
#fig,axs = qualityplot.TimesItalicModified(figsize=(9.5,4.5))(1,1)# ,**{'scheme':'nb'})
#fig,axs = qualityplot.SansModified(figsize=(9.5,4.5))(1,1)# ,**{'scheme':'nb'})
#fig,axs = qualityplot.Fonts(figsize=(9.5,4.5))(1,1)# ,**{'scheme':'nb'})
#fig,axs = qualityplot.PalatinoItalic(figsize=(9.5,4.5))(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')
legend = leg = axs.legend()
legend.get_frame().set_linewidth(1.2)
plt.setp(legend.get_texts(), color='#555555')
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/system06b.pdf')
plt.show()
