def main():
start_time = datetime.now()
#y0_sode_p1 = np.array([1.,0.,0.])
y0 = np.array([2.,1.])
# problem1 = rhs.Rhs(func01, 0.0, 2 , y0 , 30)
#y0_sode_p1 = np.array([1.,0.,0.])
#y0_sode_p2 = np.array([1.,0.])
#y0 = np.array([0.15])
problem1 = rhs.Rhs(func0, 0.0, 0.01 , y0, 20, anal0)
x,y = problem1.analiticalSolution(save=True)
#------------------------------------------------------------------------------------------
#------------------------------------------------------------------------------------------
#------------------------------------------------------------------------------------------
# fwdeuler_p1 = euler.Explicit(problem1,'fwe.dat')
# fet,feu = fwdeuler_p1.solve()
bwdeuler = impliciteuler.BWDEuler(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()
# 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()
impcn = rungekutta.ImplicitCrankNicholson(problem1, 'cn.dat')
cnt,cnu = impcn.solve()
#
# rk_p1 = implicitrungekutta.ImpRK2(problem1, 'rk.dat')
# rkt,rku = rk_p1.solve()
rk_p1 = implicitrungekutta.ImpRK4(problem1, 'rk.dat')
rkt,rku = rk_p1.solve()
radau = RadauIIA(problem1,'radIIA.dat')
rdt,rdu = radau.solve()
radau5 = RadauIIA5th(problem1,'radIIA.dat')
rd5t,rd5u = radau5.solve()
bdf = MEBDF(problem1,'bdf.dat')
bdft,bdfu = bdf.solve(1,0.5)
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',color='C1') #, linestyle=':')
#axs.plot(bet,beu,label='Imp Euler') #, linestyle=':')
axs.plot(rdt,rdu,label='Radau IIA 3rd',color='C3')
axs.plot(rd5t,rd5u,label='Radau IIA 5th',color='C2')
axs.plot(bdft,bdfu,label='BDF',color='C4')#,linestyle='--')
axs.plot(rkt,rku,label='Implicit RK4',color='C0') #,linestyle=':')
#axs.plot(rk3t,rk3u,label='Imp RK') #,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,1.5*np.exp(-x) + 0.5* np.exp(-1000*x) ,label='Analitical', marker='o',markersize=7,linestyle='',alpha=0.7, color= 'C0' ) #, linestyle=':')
axs.plot(x,1.5*np.exp(-x) - 0.5* np.exp(-1000*x), marker='o',markersize=7,linestyle='',alpha=0.7 , color= 'C0') #, 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('system02.pdf')
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, 0.85), loc=2, borderaxespad=0.)
plt.show()
def main():
start_time = datetime.now()
y0 = np.array([1., 1.])
problem1 = rhs.Rhs(func0, 0.0, 800, y0, 60, anal0, dt=0.003)
problem2 = rhs.Rhs(func0b, 0.0, 2000, y0, 60, anal0, dt=0.001)
x, y = problem1.analiticalSolution(save=True)
##----------------------------------------------------------------------------------------------------
##----------------------------------------------------------------------------------------------------
##----------------------------------------------------------------------------------------------------
# fwdeuler_p1 = euler.Explicit(problem1,'fwe.dat')
# fet,feu = fwdeuler_p1.solve()
# bwdeuler = impliciteuler.BWDEuler(problem1, 'bwe.dat')
# iet,ieu = bwdeuler.solve()
# sieuler_p1 = euler.SemiImplicit(problem1, 'bwe.dat')
# siet,sieu = sieuler_p1.solve()
#beuler = euler.Backward(problem1, 'bwe.dat')
#bt,bu = beuler.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()
# cn_p2 = rungekutta.ImplicitCrankNicholson(problem1, 'cn.dat')
# cnt,cnu = cn_p2.solve()
#
# rk_p1 = implicitrungekutta.ImpRK2(problem1, 'rk.dat')
# rkt,rku = rk_p1.solve()
# rk_p = implicitrungekutta.ImpRK4(problem1, 'rk.dat')
# rkt,rku = rk_p.solve()
radau = RadauIIA(problem2, 'radau3.dat')
rt, ru = radau.solve()
radau5 = RadauIIA5th(problem2, 'radau5.dat')
r5t, r5u = radau5.solve()
bdf = MEBDF(problem2, 'bdf.dat')
bdft, bdfu = bdf.solve(0.8, 0.6)
end_time = datetime.now()
print('Duration: {}'.format(end_time - start_time))
fig, axs = qualityplot.Fonts(**{'scheme': 'nbd'})(
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(iet,ieu,label='NR-BWDEuler') #, linestyle=':')
#axs.plot(bet,beu,label='Imp Euler') #, linestyle=':')
# axs.plot(rt,ru[:,0],label='RadauIIA')
axs.plot(r5t, r5u[:, 0], label='RadauIIA 5th 1st eq')
#axs.plot(r5t,r5u[:,1],label='RadauIIA 5th 2nd eq')
#axs.plot(cnt,cnu,label='Imp Crank Nicholson',linestyle='-')
# axs.plot(rkt,rku,label='Imp RK4') #,linestyle=':')
# axs.plot(am5t,am5u,label='Adams Moulton 5th') #,linestyle=':')
# axs.plot(am4t,am4u,label='Adams Moulton 4th') #,linestyle=':')
axs.plot(bdft, bdfu[:, 0], label='BDF')
# axs.plot(impt,impu,label='Implicit Mid-Point Method',linestyle='-.')
#axs.plot(x,y,label='Analitical', marker='o',markersize=7,linestyle='',alpha=0.7, color= 'C0' ) #, linestyle=':')
#axs.plot(x,1.5*np.exp(-x) - 0.5* np.exp(-1000*x), marker='o',markersize=7,linestyle='',alpha=0.7 , color= 'C0') #, 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('Van Der Pol Problem (Stiff system diff eq)', y=1.05)
plt.savefig('../Results/StiffSysVanDerPol_2.pdf')
plt.show()
def main():
start_time = datetime.now()
y0 = np.array([0.15])
problem1 = rhs.Rhs(func0, 0.0, 2.0 , y0, 20)
#x,y = problem1.analiticalSolution(save=True)
#------------------------------------------------------------------------------------------
#------------------------------------------------------------------------------------------
# fwdeuler = euler.Explicit(problem1,'fwe.dat')
# fet,feu = fwdeuler.solve()
# bwdeuler = euler.Implicit(problem1, 'bwe.dat')
# bet,beu = bwdeuler.solve()
impeuler = impliciteuler.BWDEuler(problem1,'impeul.dat')
iet,ieu = impeuler.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()
# impCN = rungekutta.ImplicitCrankNicholson(problem1, 'cn.dat')
# cnt,cnu = impCN.solve()
# impCN = rungekutta.ImplicitCrankNicholson(problem1, 'cn.dat')
# cnt,cnu = impCN.solve()
#
# rk4ord = implicitrungekutta.ImpRK2(problem1, 'rk.dat')
# rkt,rku = rk4ord.solve()
#
rk4ord = implicitrungekutta.ImpRK4(problem1, 'rk.dat')
rkt,rku = rk4ord.solve()
radau = RadauIIA(problem1, 'radau.dat')
rdt,rdu = radau.solve()
radau5 = RadauIIA5th(problem1, 'radau.dat')
rd5t,rd5u = radau5.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()
am5_p1 = adamsmoulton.AdamsMoulton5th(problem1, 'am5_1.dat')
#ab2_p = ab2_p1._2nd(problem1,'ab2_1.dat')
am5t,am5u = am5_p1.solve()
bdf = MEBDF(problem1 , 'bdf.dat')
bdft , bdfu = bdf.solve(1,0)
#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(iet,ieu,label='NR-BWDEuler')#, linestyle=':')
# axs.plot(bet,beu,label='Imp Euler') #, linestyle=':')
#axs.plot(iet,ieu,label='NR-Imp Euler') #, linestyle=':')
#axs.plot(lft,lfu,label='Leap Frog')
#axs.plot(cnt,cnu,label='Implicit Crank Nicholson')#,linestyle='--')
axs.plot(rkt,rku,label='Runge Kutta 4th',linestyle='-')
axs.plot(rdt,rdu,label='RadauIIA') #,linestyle=':')
axs.plot(rd5t,rd5u,label='RadauIIA') #,linestyle=':')
#axs.plot(am5t,am5u,label='Adams Moulton 5th',linestyle=':')
axs.plot(bdft,bdfu,label='BDF')
#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/StiffEq1.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()
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('system02.pdf')
plt.show()
def main():
start_time = datetime.now()
y0 = np.array([1., 0., 0])
problem1 = rhs.Rhs(func0, 0.0, 10e11, y0, 100000000)
#x,y = problem1.analiticalSolution(save=True)
##----------------------------------------------------------------------------------------------------
##----------------------------------------------------------------------------------------------------
##----------------------------------------------------------------------------------------------------
# fwdeuler_p1 = euler.Explicit(problem1,'fwe.dat')
# fet,feu = fwdeuler_p1.solve()
#bwdeuler = impliciteuler.BWDEuler(problem1, 'bwe.dat')
#iet,ieu = bwdeuler.solve()
# sieuler_p1 = euler.SemiImplicit(problem1, 'bwe.dat')
# siet,sieu = sieuler_p1.solve()
beuler = euler.Backward(problem1, 'bwe.dat')
bt, bu = beuler.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()
# cn_p2 = rungekutta.ImplicitCrankNicholson(problem1, 'cn.dat')
# cnt,cnu = cn_p2.solve()
#
# rk_p1 = rungekutta.ImplicitRK2(problem1, 'rk.dat')
# rkt,rku = rk_p1.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(iet,ieu,label='NR-BWDEuler') #, linestyle=':')
#axs.plot(bet,beu,label='Imp Euler') #, linestyle=':')
#axs.plot(lft,lfu,label='Leap Frog')
#axs.plot(cnt,cnu,label='Imp Crank Nicholson',linestyle='-')
#axs.plot(rkt,rku,label='Imp RK2') #,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',markersize=7,linestyle='',alpha=0.7, color= 'C0' ) #, linestyle=':')
#axs.plot(x,1.5*np.exp(-x) - 0.5* np.exp(-1000*x), marker='o',markersize=7,linestyle='',alpha=0.7 , color= 'C0') #, linestyle=':')
legend = leg = axs.legend()
legend.get_frame().set_linewidth(0.7)
plt.setp(legend.get_texts(), color='#555555')
plt.xscale('log')
axs.set(xlabel='time', ylabel='y(t)')
axs.set_title('dy$_1$/dt=-10(t-1)y$_1$', y=1.05)
#plt.savefig('system02.pdf')
plt.show()
