MATLAB: Reduce computational time for ODE solver

MATLABode solverode systemode23

Hi all
i have this code
for iDom_hot = 1:numel(Dall_hot)
    xRange_hot = Dall_hot{iDom_hot};
for iInitial_hot = 1:numel(Y0_Lhot)
            Mach_hot=Mach_cell_hot{iInitial_hot};
            Tw_hot=Tnew_cell_hot{iDom_hot};
            Ch_hot=ChL_cell_hot{iDom_hot,iInitial_hot};
            Fc_hot=fL_cell_hot{iDom_hot,iInitial_hot};   
            Hrrj_hot=hrrj_cell_hot{iDom_hot};
            Aeff_hot=Aeff_cell_hot{iDom_hot,iInitial_hot};
            Perim_hot=Perim_cell_hot{iDom_hot,iInitial_hot};
            L_Ength_hot=L_cell_hot{iDom_hot};
            Pend_chamb_hot=Pressure_ED_chamber_cell_hot{iDom_hot};
         if Ch_hot>0&&Fc_hot>0&&Hrrj_hot>0&&Tw_hot>0 &&Mach_hot>0&&Perim_hot>0&&Aeff_hot>0&&L_Ength_hot>0&&Pend_chamb_hot>0
             
    [xSol_hot{iDom_hot,iInitial_hot},YSol_L_hot{iDom_hot,iInitial_hot}]=ode23(@(x,Y)...
            chambesinglebobbTWVARIABILEHOT(x,Y,Ch_hot,Aeff_hot,Perim_hot,Fc_hot,Tw_hot),xRange_hot,Y0_Lhot{iInitial_hot});  
        if(any(YSol_L_hot{iDom_hot,iInitial_hot}(:,3)>0.8))
      disp([ ' condizione verificata'])
      disp (iDom_hot)
      disp(iInitial_hot)
      
     break    
   end     
         end
         
   
   
            
end
           
end
that solve iteratively an ODE system:
function dYdx=tubosinglebobb(x,Y,Ch_hot,Aeff_hot,Perim_hot,Fc_hot,Tw_hot)
gamma=1.667;
Dexttantalum=0.001500000000000;
Tt=Y(1);
Pt=Y(2);
M=Y(3);
dTtdx=Ch_hot*(Tw_hot-Tt)*(Perim_hot/Aeff_hot);
dPtdx=Pt*((-gamma*((M^2)/2)*Fc_hot*(Perim_hot/Aeff_hot))-...
    (gamma*((M^2)/2)*dTtdx*(1/Tt)));
dMdx=M*(((1+((gamma-1)/2)*M^2)/(1-M^2))*((gamma*(M^2)*Fc_hot*...
    Perim_hot)/(2*Aeff_hot))+...
    ((0.5*((gamma*M^2)+1))*(1+((gamma-1)/2)*M^2)/(1-M^2))*...
    (Ch_hot*(Tw_hot-Tt)*Perim_hot)/(Aeff_hot*Tt));
dYdx=[dTtdx;dPtdx;dMdx];
end
the computational time for solving the ODE system is very very large (days) due to ( i think) one problem. In particular:
numel(Dall_ho) is more or less equal to 700, while numel(Y0_Lhot) is equal to 30, those domains dimensions should not be problematic, the real problem is on the oscillation of the solution YSol_L_hot when its third column reach value around 1. I have prepared a break for this eventuality but doesn't seem to reduce computational time!! I don't really know which is the problem, could it be a syntax error?
Thank you all for the help
Regards

Best Answer

Have you tried the other ODE-integrating functions? From your problem description it sounds like your ODEs are stiff - for that ode23 is not the optimal function, perhaps you get much better success with ode15s or oed23s that both are designed for stiff ODEs. One further note is that to me it seems like the temperature-derivative does not depend on the other 2 parameters, perhaps you can refactor the problem to first integrate that ODE and then use that solution when integrating the other 2.
Related Question