Help to speed up the code

Hello everyone, I need to speed up this simulation code because it took around several hours, can somebody help me how to speed it up?

pc=3.16;               
T=293;                  
rwc3s=0.47;             
rwc2s=0.27;
rwc3a=0.10;            
rwc4af=0.09;
mc=0.4;                
mw=0.157;               
ms=0.658;             
mg=1.129;              
wc=mw/mc;              
vc=1/((wc*pc)+1);     
ro=(3*vc/(4*pi))^1/3;  
%% Proposed Model
yg=0.25;            
yw=0.15;            
RH=0.88;            
b1=1231;            
b2=7579;            
B293=0.3*10^-10;    
C=5*10^7;           
ER=5364;            
De293=((rwc3s*100)^2.024)*(3.2*10^-14);                 
kr293=(8.05*(10^-10))*((rwc3s*100+rwc3a*100)^0.975);    
v=2.06;                                                
cw=((RH-0.75)/0.25)^3;                                  
pw=1;
%De=De293*exp(-b2*(1/T-1/293));                         
B=B293*exp(-b1*(1/T-1/293));                           
kr=kr293*exp(-ER*(1/T-1/293));                         
%% Determine the day
hr=15;                                                  
da=24*hr;                                             
dt=1;                                             
Nn=(da)*(1/dt);                                      
time=1:Nn;
time2=1:Nn+1;
%% Simulation MC
n=100000;      %this is the number of trial                                          
rlower=0.5;
rupper=125;                                             
r_initial=rlower+(rupper-rlower)*rand(1,n);                      

m=length(r_initial);
n1=length(time);
%% Pre-allocation speed
n2=length(time2);
Sr=zeros(1,n1);
cst=zeros(1,n1);
alfa=zeros(1,n1);
kd=zeros(1,n1);
De=zeros(1,n1);
rt_inc=zeros(1,n1);
Rt_inc=zeros(1,n1);
Alfa=zeros(m,n1);
Rt_inc1=zeros(m,n1);
rt_inc1=zeros(m,n1);
ro_init1=zeros(m,1);
alfag1=zeros(m,n1);
Vdp1=zeros(m,1);
vdp1=zeros(m,1);

for i = 1:m  
ro_init=r_initial(i)*0.001;                 
L=((4*pi*(wc*pc/pw+1)/3)^(1/3))*ro_init;      


    for AA=1:Nn
        if (AA==1)
            rt_inc(1)=ro_init(1)-0.00001;   %boundary condition 
            Rt_inc(1)=ro_init(1)+0.00001;   %boundary condition 
        else
            rt_inc(1)=ro_init(1)-0.00001;
            Rt_inc(1)=ro_init(1)+0.00001;
        end
    end

    for BB=1:Nn
        if Rt_inc(BB)/L<=ro
            Sr(BB)=0;
        elseif (Rt_inc(BB)/L>=ro)&&(Rt_inc(BB)/L<0.5)
            Sr(BB)=4*pi*(Rt_inc(BB)/L)^2;
        elseif (0.5<=Rt_inc(BB)/L)&&(Rt_inc(BB)/L<0.5*(2^0.5))
            Sr(BB)=(4*pi*(Rt_inc(BB)/L)^2)-(6*pi*(1-(0.5/(Rt_inc(BB)/L))));
        elseif (Rt_inc(BB)/L>=0.5*(2^0.5)) && (Rt_inc(BB)/L<0.5*(3^0.5))
            syms y x
            fun = @(y,x) 8*(Rt_inc(BB)/L)./(sqrt((Rt_inc(BB)/L)^2-(x.^2)-(y.^2)));
            ymin=sqrt((Rt_inc(BB)/L)^2-0.5);
            xmin=@(x) sqrt((Rt_inc(BB)/L)^2-0.25-x.^2);
            Sr(BB)=integral2(fun,ymin,0.5,xmin,0.5);
        else
            Sr(BB)=0;
        end
        cst(BB)=Sr(BB)/(4*pi*Rt_inc(BB)^2);
        alfa(BB)=1-(rt_inc(BB)/ro_init)^3;
        kd(BB)=(B/(alfa(BB)^1.5))+C*(Rt_inc(BB)-ro_init)^4;
        De(BB)=De293*(log(1/alfa(BB)))^1.5;
        rt_inc(BB+1)=rt_inc(BB)-(dt*((pw*cst(BB)*cw)/((yw+yg)*pc*rt_inc(BB)^2))*1/((1/(kd(BB)*rt_inc(BB)^2))+(((1/rt_inc(BB))-(1/Rt_inc(BB)))/De(BB))+(1/(kr*rt_inc(BB)^2))));
        Rt_inc(BB+1)=((v-1)*((rt_inc(BB)^2)/(Rt_inc(BB)^2))*((rt_inc(BB)-rt_inc(BB+1))/dt))*dt+Rt_inc(BB);
    end

Sr1(i,:)=Sr;
Alfa(i,:) = alfa ; 
Rt_inc1(i,:) = Rt_inc(1:n1);
rt_inc1(i,:) = rt_inc(1:n1);
rt_inc2(i,:) = rt_inc;
ro_init1(i,:)= ro_init;

b=0.0517;                                                    
n=1.0145;% 0.6;                                              
Vdp=(1-exp(-b*((2*ro_init*1000)^n)));                       
vdp=2*b*n*exp(-b*(2*ro_init*1000)^n)*(2*ro_init*1000)^(n-1); 

N=6*(10^12)*mc*vdp/(pc*pi*(2*ro_init*1000)^3);              
alfag=alfa*vdp;

alfag1(i,:)=alfag;

Vdp1(i,:)=Vdp;
vdp1(i,:)=vdp;
N1(i,:)=N;
end

Thankyou in advance.

Best Regads,

Kevin

Answer 1

[Durganshu]

Well, the code inside the loops can be edited and vectorized to obtain faster results. I would suggest you go through this documentation on vectorization that may help you:

https://in.mathworks.com/help/matlab/matlab_prog/vectorization.html

[Kevin Isakayoga]

Could you help me to modify it? because I am not good in the implementation, I will be grateful if you can help me. Thankyou very much!

[Durganshu]

Sorry for a late reply. I'm actually quite busy. i'll try to speed up your code when I'm free.