MATLAB: Avoid divergent curves of ODE solutions

divergenceinstabilityodeode23tplot

Hi all
I have solved a system of differential equations in an iterative way, as you can see from the graph I have several curves each of which is associated with a different combination of the iterative parameters. Again from the graph, it can be seen that some curves at a certain abscissa diverge; this is not acceptable so I would like to remedy it. Is it possible to create a new solution vector capable of avoiding the divergence as described below ?
I would like the solution not to diverge near the various cusp points and, on the contrary, to maintain the value immediately upstream of the latter, until the end of the domain. I'll explain: suppose we have the following solution values 1000 K,1020 K,2000 K,4000 K I would like instead: 1000 K,1020 K,1020 K,1020 K
Thank you for the help
Regards
T0=293;
delta_Thot=2500;%s 
%%%%%%%%%%%%%
Nc_Thot=2;
[ya,sa,lea]=size(Aexposehot);
for y=1:yV%passo,altezza tubo,Rextbobbin,lunghezza cavo
    for le=1:leV%lunghezza tubo equilibrio
                for sv=1:sV%spessore parete3
                  % for k=1:km%Mach 
                   for rf=1:length(Pressure_percentage_hot)
Rextbobb_cellhot(y)={Rextbobbin_fluxhot(y)};
Y0hot(y,le)={[T0,m0hot(y,le)]};
Dall_Th_hot ={[0:Nc_Thot:delta_Thot]};        
Lequilibrium_cellhot(le)={Lequilibriumhot(le)};        
Passo_cellhot(y)={Passo_fluxhot(y)}; 
hrad_cellhot(y)={Hradial_fluxhot(y)};
Spessore_parete3_cellhot(sv) ={Spessore_parete3hot(sv)};
Aexpose_cellhot(y,sv,le)={Aexposehot(y,sv,le)};
Volume_cell_Aisihot(le,y,sv)={Volume_Aisihot(le,y,sv)};
Volume_cell_gashot(y,le)={Volume_gashot(y,le)};
throat_cell_hot(y)={ThrtR_fluxhot(y)};
Pressure_end_chamber_hot_cell(rf)={Pressure_end_chamber_hot(rf)};
                   end
end    
end
  end
for iDom_Th = 1:numel(Dall_Th_hot)
   for leLE=1:numel(Lequilibrium_cellhot)
       for yY=1:numel(hrad_cellhot)
               for rF=1:numel(Pressure_end_chamber_hot_cell)
                  for sS=1:numel(Spessore_parete3_cellhot)
TSol_hot(iDom_Th,yY,leLE,sS,rF)={zeros(length(Dall_Th_hot{iDom_Th}),2)};
    end
    end 
    end
    end
   end 
opt_t_hot=odeset('NormControl','Refine','Stats','MaxStep');
for iDom_Th = 1:numel(Dall_Th_hot)
    tRange_hot = Dall_Th_hot{iDom_Th};
         for leLE=1:numel(Lequilibrium_cellhot)
                 for yY=1:numel(hrad_cellhot)
                       for rF=1:numel(Pressure_end_chamber_hot_cell)
                         for sS=1:numel(Spessore_parete3_cellhot)
 
                           Ltube_hot= Lequilibrium_cellhot{leLE};%L_cellhot{yY}; 
                           Leq_hot= Lequilibrium_cellhot{leLE} ;   
                           Vol_Aisi_hot=Volume_cell_Aisihot{leLE,yY,sS};
                           Aexp_hot=Aexpose_cellhot{yY,sS,leLE};
                           Hradial_hot=hrad_cellhot{yY};
                           ThroatradiuS_hot=throat_cell_hot{yY};
                           Pressure_hot_end_chamber=Pressure_end_chamber_hot_cell{rF};
                 if Vol_Aisi_hot>0&&Leq_hot>0 &&Aexp_hot>0 &&Ltube_hot>0 && ThroatradiuS_hot>0&&Pressure_hot_end_chamber>0  
    [tSol{iDom_Th,yY,leLE,sS,rF},TSol_hot{iDom_Th,yY,leLE,sS,rF}]=ode23t(@(t,Y) ...
            temperaturaheaterclassica(t,Y,Ltube_hot,Voltage1,Vol_Aisi_hot,Aexp_hot,ThroatradiuS_hot,Pressure_hot_end_chamber),tRange_hot,Y0hot{yY,leLE},opt_t_hot);
        if(any(TSol_hot{iDom_Th,yY,leLE,sS,rF}(:,1)>1600))
       %      disp([ ' condizione verificata'])
      %disp (iDom_Th)
      disp(yY)
      disp(leLE)
      %disp(sS)
      %disp(rF)
     break    
        end   
          
                         end
                      end
                    end
                 end
         end
end
    
%end
[tT,yT,leT,sT,rFT]=size(TSol_hot);
for t = 1:tT
    for y=1:yT
         for le=1:leT
                 for s=1:sT
                      for rf=1:rFT
     if TSol_hot{t,y,le,s,rf}(end,1)>0
        
                                
figure(1);set(gcf,'Visible', 'on')
plot(tSol{t,y,le,s,rf}(:,1),TSol_hot{t,y,le,s,rf}(:,1))
xlabel('time [s]')
ylabel('Teq-transition/turbulent [K]')    
hold on
end
end
end
end
end
end

Best Answer

The divergence of an ode system could be due to two things: on one hand the system itself is devergent, this is due to the combination of parameter you are giving to the ode. On the other hand, it could be that the integrator is not suitable or correctly configurated to solve that syste. To test this you could use different integrators as: ode45, ode23, ode113, ode15s, ode23t, ode23b or ode23tb. I suggest ode15s is very robust.
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