Example #1
0
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()
Example #2
0
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([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()
Example #4
0
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()