Array indices must be positive integers or logical values.

Hi all I have the above error, could you please help me to know the problem. THANK YOU.

xl=0; xr=1;            %domain[xl,xr]                                                                                                                         
J=100;                  % J: number of dividion for x
dx=(xr-xl)/J;          % dx: mesh size
ds=dx;
tf=10;                % final simulation time
Nt=100; %Nt=100000;                 %Nt:number of time steps
dt=tf/Nt;                                                                                     
%c=50;     
%s=600;   % paremeter for the solution
lambdau1=0.008;          %turning rate of susp(right)
lambdau2=0.008;          %turning rate of susp(left)
lambdav1=0.005;           %turning rate of infect(right)
lambdav2=0.005;           %turning rate of infect(left)
beta=0.04;               % transimion rate
alpha=0.6;               %recovery/death rate
b=6;
d=3;
bV=3;
dV=5;
au=0.01;                   % advection speed - susceptible
av=0.001;                   % advection speed - infected
A=0.1;
mu1=au*dt/dx; 
mu2=av*dt/dx;  
if mu1>1.0               %make sure dt satisfy stability condition
    error('mu1 should<1.0!')
end
if mu2>1.0               %make sure dt satisfy stability condition
    error('mu2 should<1.0!')
end
%Evaluate the initial conditions 
x=xl:dx:xr;                   %generate the grid point
%fr=0*exp(-c*(x-0.5).^2);     %dimension f(1:J+1)initial conditions of right moving suscp
%fl=0*exp(-c*(x-0.5).^2);    %initial conditions of left moving suscep
%gr=0.5*exp(-s*(x-0.5).^2);  %initial conditions of infected
%gl=0.5*exp(-s*(x-0.5).^2);  %initial conditions of infected
kk=6*pi/(xr-xl);
%fr=0.0+0.01*(1+sin(k*x));     %dimension f(1:J+1)initial conditions of right moving suscp
%fl=0.001+0.01*(1+sin(k*x));    %initial conditions of left moving suscep
fr =  7.5 + 0.001*(1+sin(kk*x));
fl =  7.5 + 0.001*(1+sin(kk*x));
gr =  0.0 + 0.001*(1+sin(kk*x));  %initial conditions of infected
gl =  0.0 + 0.001*(1+sin(kk*x));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
k1=6*pi/(xr-xl);
X=k1*ds;
for ii=1:J+1
    Sr =     7.5 + 0.001*(1+sin(X*ii));
    Sl =     7.5 + 0.001*(1+sin(X*ii));
    Ir =     0.0 + 0.001*(1+sin(X*ii));  %initial conditions of infected
    Il =     0.0 + 0.001*(1+sin(X*ii));
end
%store the solution at all grid points for all time steps
ur=zeros(J+1,Nt);
ul=zeros(J+1,Nt);
vr=zeros(J+1,Nt);
vl=zeros(J+1,Nt);
v=zeros(J+1,Nt);
I=zeros(J+1,Nt);
W=zeros(J+1,Nt);
Z=zeros(J+1,Nt);
U=zeros(J+1,Nt);
I1=zeros(J+1,Nt);
W1=zeros(J+1,Nt);
U1=zeros(J+1,Nt);
Z1=zeros(J+1,Nt);
II=zeros(J+1,Nt);
WW=zeros(J+1,Nt);
ZZ=zeros(J+1,Nt);
UU=zeros(J+1,Nt);
II1=zeros(J+1,Nt);
WW1=zeros(J+1,Nt);
ZZ1=zeros(J+1,Nt);
UU1=zeros(J+1,Nt);
y1=zeros(J+1,Nt);
y2=zeros(J+1,Nt);
y3=zeros(J+1,Nt);
y4=zeros(J+1,Nt);
Q1=zeros(J+1,Nt);
Q2=zeros(J+1,Nt);
Q3=zeros(J+1,Nt);
Q4=zeros(J+1,Nt);
F1=zeros(J+1,Nt);
F2=zeros(J+1,Nt);
F3=zeros(J+1,Nt);
F4=zeros(J+1,Nt);
P1=zeros(J+1,Nt);
P2=zeros(J+1,Nt);
P3=zeros(J+1,Nt);
P4=zeros(J+1,Nt);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
tt=0:tf/(Nt-1):tf;
[T,X]=meshgrid(tt,x);
%s=0.05;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
wb = waitbar(0, 'please wait (N)');
cleanMe = onCleanup(@() delete(wb));
%find the approximate solution at each time step 
for  n=1:Nt
    waitbar(n/Nt, wb);
    t=n*dt;               % current time
    if n==1                         % first time step
        
        KU0 =    1 ./ (0.05 .* sqrt(2*pi)) .* exp(-0.5*(0./0.05).^2 );
        KU =  @(m)  1 ./ (0.05 .* sqrt(2*pi)) .* exp(-0.5*(m./0.05).^2 );
        bKU =  -b .* (Ir+Il);
        y1 =   bKU + d.* Sr ;
        y2 =   bKU+ d.* Sl;
        Q1=    bKU + d.* Sr;
        Q2 =   bKU + d.* Sl;
        KV0 =  1 ./ (0.01 .* sqrt(2*pi)) .* exp(-0.5*(0./0.01).^2 );
        KV = @(m) 1 ./ (0.01 .* sqrt(2*pi)) .* exp(-0.5*(m./0.01).^2 );
        bKV =   -bV  .* (Ir+Il);
        F1 =   bKV + d .* Sr ;
        F2 =   bKV + d .* Sl;
        P1=   bKV + d .* Sr;
        P2=    bKV + d .* Sl;
        for i=1:J+1 
            sum=0;   
            sum1=0;
            sum2=0;
            sum3=0;
            for k=1:J 
                if ((i+k-J)>=1)
                    sum=sum+2*KU0*y1((i+k)-(J+1));
                    sum1=sum1+2*KU0*y2((i+k)-(J+1));
                    sum2=sum2+2*KV0*F1((i+k)-(J+1));         
                    sum3=sum3+2*KV0*F2((i+k)-(J+1));
                end
            end
            I(i) = ds/2*(2*KU(ds*(J+1))*2*y1(i)+sum+2*KU(ds*(J+1)));
            W(i) = ds/2*(2*KU(ds*(J+1))*2*y2(i)+sum1+2*KU(ds*(J+1)));
            Z(i) = ds/2*(KV(ds*(J+1))*2*F1(i)+sum2+KV(ds*(J+1)));
            U(i) = ds/2*(KV(ds*(J+1))*2*F2(i)+sum3+KV(ds*(J+1)));     
            
        end 
        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        for i=1:J+1 
            sum4=0;
            sum5=0;
            sum6=0;
            sum7=0;
            for k=1:J 
                if (i-k<=0)
                    sum4=sum4+2*KV0*Q1(J+1+(i-k));
                    sum5=sum5+2*KV0*Q2(J+1+(i-k));
                    sum6=sum6+2*KV0*P1(J+1+(i-k));
                    sum7=sum7+2*KV0*P2(J+1+(i-k));
                else
                    if (i-k>0) 
                        sum4=sum4+2*KV0*Q1(i-k);  
                        sum5=sum5+2*KV0*Q2((i-k));
                        sum6=sum6+2*KV0*P1((i-k));
                        sum7=sum7+2*KV0*P2((i-k));
                    end
                end
            end
            II(i)=ds/2*(KU(-ds*(J+1))*2*Q1(i)+sum4+KU(-ds*(J+1)));
            WW(i)=ds/2*(KU(-ds*(J+1))*2*Q2(i)+sum5+KU(-ds*(J+1)));
            ZZ(i)=ds/2*(KV(-ds*(J+1))*2*P1(i)+sum6+KV(-ds*(J+1)));
            UU(i)=ds/2*(KV(-ds*(J+1))*2*P2(i)+sum7+KV(-ds*(J+1)));
            
            
        end 
        for j=2:J                      % interior nodes
            %%%%%%%%%%%%%%%%%%%upwind of right-moving of susceptible
            ur(j,n)=fr(j)-0.5*mu1*(fr(j)-fr(j-1))+dt*lambdau2*(0.5+0.5*tanh(1+(I(j)+II(j))))*fl(j)-dt*lambdau1*(0.5+0.5*tanh(1+(W+WW)))*fr(j)-dt*beta*fr(j)*(gr(j)+gl(j))+dt*0.5*alpha*(gr(j)+gl(j));
            %%%%%%%%%%%%%%%%%%%upwind of left-moving of susceptible
            ul(j,n)=fl(j)+0.5*mu1*(fl(j+1)-fl(j))+dt*lambdau1*(0.5+0.5*tanh(1+(W(j)+WW(j))))*fr(j)-dt*lambdau2*(0.5+0.5*tanh(1+(I(j)+II(j))))*fl(j)-dt*beta*fl(j)*(gr(j)+gl(j))+dt*0.5*alpha*(gr(j)+gl(j));
            %%%%%%%%%%%%%%%%%%%upwind of right-moving of infected
            vr(j,n)=gr(j)-0.5*mu2*(gr(j)-gr(j-1))+dt*lambdav2*(0.5+0.5*tanh(1+(ZZ(j)+Z(j))))*gl(j)-dt*lambdav1*(0.5+0.5*tanh(1+(U(j)+UU(j))))*gr(j)+dt*beta*fr(j)*(gr(j)+gl(j))-dt*alpha*gr(j);
            %%%%%%%%%%%%%%%%%%%lupwind of left-moving of infected
            vl(j,n)=gl(j)+0.5*mu2*(gl(j+1)-gl(j))+dt*lambdav1*(0.5+0.5*tanh(1+(U(j)+UU(j))))*gr(j)-dt*lambdav2*(0.5*+0.5*tanh(1+(ZZ(j)+Z(j))))*gl(j)+dt*beta*fl(j)*(gr(j)+gl(j))-dt*alpha*gl(j);
            
            
        end
        %peridic BC for right moving of suscep(j=J+1,j+2=1)     
        ur(J+1,1)= fr(J+1)-0.5*mu1*(fr(J+1)-fr(J))+dt*lambdau2*(0.5+0.5*tanh(1+(I(J+1)+II(J+1))))*fl(J+1)-dt*lambdau1*(0.5+0.5*tanh(1+(W(J+1)+WW(J+1))))*fr(J+1)-dt*beta*fr(J+1)*(gr(J+1)+gl(J+1))+dt*0.5*alpha*(gr(J+1)+gl(J+1)); 
        %peridic BC for right moving of suscep(j=1,0=J)
        ur(1,1)=fr(1)-0.5*mu1*(fr(1)-fr(J))+dt*lambdau2*(0.5+0.5*tanh(1+(II(1)+I(1))))*fl(1)-dt*lambdau1*(0.5+0.5*tanh(1+(W(1)+WW(1))))*fr(1)-dt*beta*fr(1)*(gr(1)+gl(1))+dt*0.5*alpha*(gr(1)+gl(1)); %peridic BC for right moving
        %peridic BC for left moving of suscep(j=1)
        ul(1,1)=fl(1)+0.5*mu1*(fl(2)-fl(1))+dt*lambdau1*(0.5+0.5*tanh(1+(W(1)+WW(1))))*fr(1)-dt*lambdau2*(0.5*+0.5*tanh(1+(I(1)+II(1))))*fl(1)-dt*beta*fl(1)*(gr(1)+gl(1))+dt*0.5*alpha*(gr(1)+gl(1)); %peridic BC for left moving;  %peridic BC for left moving
        %peridic BC for left moving of suscep(j=J+1)
        ul(J+1,1)=fl(J+1)+0.5*mu1*(fl(1)-fl(J+1))+dt*lambdau1*(0.5+0.5*tanh(1+(W(J+1)+WW(J+1))))*fr(J+1)-dt*lambdau2*(0.5*+0.5*tanh(1+(I(J+1)+II(J+1))))*fl(J+1)-dt*beta*fl(J+1)*(gr(J+1)+gl(J+1))+dt*0.5*alpha*(gr(J+1)+gl(J+1));  %peridic BC for right moving(j=J+1);  %peridic BC for left moving
        %peridic BC for right moving of infected(j=J+1)
        vr(J+1,1)=gr(J+1)-0.5*mu2*(gr(J+1)-gr(J))+dt*lambdav2*(0.5+0.5*tanh(1+Z(J+1)+ZZ(J+1)))*gl(J+1)-dt*lambdav1*(0.5+0.5*tanh(1+(U(J+1)+UU(J+1))))*gr(J+1)+dt*beta*fr(J+1)*(gr(J+1)+gl(J+1))-dt*alpha*gr(J+1);
        %peridic BC for right moving of infected(j=1)
        vr(1,1)=gr(1)-0.5*mu2*(gr(1)-gr(J))+dt*lambdav2*(0.5+0.5*tanh(1+(Z(1)+ZZ(1))))*gl(1)-dt*lambdav1*(0.5+0.5*tanh(1+(U(1)+UU(1))))*gr(1)+dt*beta*gr(1)*(gr(1)+gl(1))-dt*alpha*gr(1);
        %peridic BC for left moving of infected(j=1)
        vl(1,1)=gl(1)+0.5*mu2*(gl(2)-gl(1))+dt*lambdav1*(0.5+0.5*tanh(1+(U(1)+UU(1))))*gr(1)-dt*lambdav2*(0.5*+0.5*tanh(1+(Z(1)+ZZ(1))))*gl(1)+dt*beta*fl(J+1)*(gr(1)+gl(1))-dt*alpha*gl(1);
        %peridic BC for left moving of infected(j=J+1)
        vl(J+1,1)=gl(J+1)+0.5*mu2*(gl(1)-gl(J+1))+dt*lambdav1*(0.5+0.5*tanh(1+(U(J+1)+UU(J+1))))*gr(J+1)-dt*lambdav2*(0.5*+0.5*tanh(1+(Z(J+1)+ZZ(J+1))))*gl(J+1)+dt*beta*fl(J+1)*(gr(J+1)+gl(J+1))-dt*alpha*gl(J+1);
        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
        for j=1:J+1
            Sr=ur(j,n);
            Sl=ul(j,n);
            Il=vl(j,n);
            Ir=ur(j,n);
        end
    else
        KU = @(m) 1 ./ (0.05 .* sqrt(2*pi)) .* exp(-0.5*(m./0.05).^2 );
        bKU2 =   -b .* (vr(j,n)+vl(j,n));
        y3 =   bKU2 + d .*  ur(j,n);
        y4 =   bKU2 + d .* ul(j,n);
        Q3 =   bKU2 + d .*  ur(j,n);   
        Q4 =   bKU2 + d .* ul(j,n);
        KV = @(m) 1 ./ (0.01 .* sqrt(2*pi)) .* exp(-0.5*(m./0.01).^2 );
        bKV2 = -bV .* (vr(j,n)+vl(j,n));
        F3 =   bKV2 + d .*  ur(j,n);
        F4 =   bKV2 + d .*ul(j,n);
        P3 =   bKV2 + d .*  ur(j,n);
        P4 =   bKV2 + d .*ul(j,n);    
        for i=1:J+1 
            sum8=0;
            sum9=0;
            sum10=0;
            sum11=0;
            for k=1:J 
                if (i+k>=J+1)
                    sum8=sum8+2*KU(ds*k)*y3(J+1-(i+k));
                    sum9=sum9+2*KU(ds*k)*y4(J+1-(i+k));
                    sum10=sum10+2*KV(ds*k)*F3(J+1-(i+k));
                    sum11=sum11+2*KV(ds*k)*F4(J+1-(i+k));
                end          
            end 
            I1(i,n-1)=ds/2*(KU(ds*(J+1))*2*y3(i)+sum8+KU(ds*(J+1)));
            W1(i,n-1)=ds/2*(KU(ds*(J+1))*2*y4(i)+sum9+KU(ds*(J+1)));
            Z1(i,n-1)=ds/2*(KV(ds*(J+1))*2*F3(i)+sum10+KV(ds*(J+1)));
            U1(i,n-1)=ds/2*(KV(ds*(J+1))*2*F4(i)+sum11+KV(ds*(J+1)));                
        end
        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        for i=1:J+1 
            sum8=0;
            sum9=0;
            sum10=0;
            sum11=0;
            for k=1:J 
                if (i-k<=0)
                    sum8=sum8+2*KU(-ds*k)*Q3(J+1+(i-k));
                    sum9=sum9+2*KU(-ds*k)*Q4(J+1+(i-k));
                    sum10=sum10+2*KV(-ds*k)*P3(J+1+(i-k));
                    sum11=sum11+2*KV(-ds*k)*P4(J+1+(i-k));
                else
                    if (i-k>0) 
                        sum8=sum8+2*KU(-ds*k)*Q3(i-k);  
                        sum9=sum9+2*KU(-ds*k)*Q4((i-k));
                        sum10=sum10+2*KV(-ds*k)*P3((i-k));
                        sum11=sum11+2*KV(-ds*k)*P4((i-k));
                    end
                end
            end        
            II1(i)=ds/2*(KU(-ds*(J+1))*2*Q3(i)+sum8+KU(-ds*(J+1)));
            WW1(i)=ds/2*(KU(-ds*(J+1))*2*Q4(i)+sum9+KU(-ds*(J+1)));
            ZZ1(i)=ds/2*(KV(-ds*(J+1))*2*P3(i)+sum10+KV(-ds*(J+1)));
            UU1(i)=ds/2*(KV(-ds*(J+1))*2*P4(i)+sum11+KV(-ds*(J+1)));
            
        end     
        for j=2:J                % interior nodes
            %%%%%%%%%%%%%%%%%%%upwind of right-moving of susceptible
            ur(j,n)=ur(j,n-1)-0.5*mu1*(ur(j,n-1)-ur(j-1,n-1))+dt*lambdau2*(0.5+0.5*tanh(1+(I1(j,n-1)+II1(j,n-1))))*ul(j,n-1)-dt*lambdau1*(0.5+0.5*tanh(1+(W1(j,n-1)+WW1(j,n-1))))*ur(j,n-1)-dt*beta*ur(j,n-1)*(vr(j,n-1)+vl(j,n-1))+dt*0.5*alpha*(vr(j,n-1)+vl(j,n-1));
            %%%%%%%%%%%%%%%%%%%upwind of right-moving of susceptible
            ul(j,n)=ul(j,n-1)+0.5*mu1*(ul(j+1,n-1)-ul(j,n-1))+dt*lambdau1*(0.5+0.5*tanh(1+(W1(j,n-1)+WW1(j,n-1))))*ur(j,n-1)-dt*lambdau2*(0.5*+0.5*tanh(1+(I1(j,n-1)+II1(j,n-1))))*ul(j,n-1)-dt*beta*ul(j,n-1)*(vr(j,n-1)+vl(j,n-1))+dt*0.5*alpha*(vr(j,n-1)+vl(j,n-1));    
            %%%%%%%%%%%%%%%%%%%upwindof right-moving of infected
            vr(j,n)=vr(j,n-1)-0.5*mu2*(vr(j,n-1)-vr(j-1,n-1))+dt*lambdav2*(0.5+0.5*tanh(1+(Z1(j,n-1)+ZZ1(j,n-1))))*vl(j,n-1)-dt*lambdav1*(0.5+0.5*tanh(1+(U1(j,n-1)+UU1(j,n-1))))*vr(j,n-1)+dt*beta*ur(j,n-1)*(vr(j,n-1)+vl(j,n-1))-dt*alpha*vr(j,n-1);
            %%%%%%%%%%%%%%%%%%%upwind of left-moving of infected
            vl(j,n)=vl(j,n-1)+0.5*mu2*(vl(j+1,n-1)-vl(j,n-1))+dt*lambdav1*(0.5+0.5*tanh(1+(U1(j,n-1)+UU1(j,n-1))))*vr(j,n-1)-dt*lambdav2*(0.5*+0.5*tanh(1+(Z1(j,n-1)+ZZ1(j,n-1))))*vl(j,n-1)+dt*beta*ul(j,n-1)*(vr(j,n-1)+vl(j,n-1))-dt*alpha*vl(j,n-1);
            
        end 
        %peridic BC for right moving of suscep(j=J+1,j+2=1)
        ur(J+1,n)=ur(J+1,n-1)-0.5*mu1*(ur(J+1,n-1)-ur(J,n-1))+dt*lambdau2*(0.5+0.5*tanh(1+(I1(J+1,n-1)+II1(J+1,n-1))))*ul(J+1,n-1)-dt*lambdau1*(0.5+0.5*tanh(1+(W1(J+1,n-1)+WW1(J+1,n-1))))*ur(J+1,n-1)-dt*beta*ur(J+1,n-1)*(vr(J+1,n-1)+vl(J+1,n-1))+dt*0.5*alpha*(vr(J+1,n-1)+vl(J+1,n-1));
        %peridic BC for right moving of suscep(j=1,0=J)
        ur(1,n)=ur(1,n-1)-0.5*mu1*(ur(1,n-1)-ur(J,n-1))+dt*lambdau2*(0.5+0.5*tanh(1+(I1(1,n-1)+II1(1,n-1))))*ul(1,n-1)-dt*lambdau1*(0.5+0.5*tanh(1+(W1(1,n-1)+WW1(1,n-1))))*ur(1,n-1)-dt*beta*ur(1,n-1)*(vr(1,n-1)+vl(1,n-1))+dt*0.5*alpha*(vr(1,n-1)+vl(1,n-1));
        %peridic BC for left moving of suscep (j=1)
        ul(1,n)=ul(1,n-1)+0.5*mu1*(ul(2,n-1)-ul(1,n-1))+dt*lambdau1*(0.5+0.5*tanh(1+(W1(1,n-1)+WW1(1,n-1))))*ur(1,n-1)-dt*lambdau2*(0.5*+0.5*tanh(1+(I1(1,n-1)+II1(1,n-1))))*ul(1,n-1)-dt*beta*ul(1,n-1)*(vr(1,n-1)+vl(1,n-1))+dt*0.5*alpha*(vr(1,n-1)+vl(1,n-1));    
        %peridic BC for left moving of suscep(j=J+1)
        ul(J+1,n)=ul(J+1,n-1)+0.5*mu1*(ul(1,n-1)-ul(J+1,n-1))+dt*lambdau1*(0.5+0.5*tanh(1+(W1(J+1,n-1)+WW1(J+1,n-1))))*ur(J+1,n-1)-dt*lambdau2*(0.5*+0.5*tanh(1+(I1(J+1,n-1)+I1(J+1,n-1))))*ul(J+1,n-1)-dt*beta*ul(J+1,n-1)*(vr(J+1,n-1)+vl(J+1,n-1))+dt*0.5*alpha*(vr(J+1,n-1)+vl(J+1,n-1));    
        %peridic BC for right moving of infected(j=J+1)
        vr(J+1,n)=vr(J+1,n-1)-0.5*mu2*(vr(J+1,n-1)-vr(J,n-1))+dt*lambdav2*(0.5+0.5*tanh(1+(Z1(J+1,n-1)+ZZ1(J+1,n-1))))*vl(J+1,n-1)-dt*lambdav1*(0.5+0.5*tanh(1+(U1(J+1,n-1)+UU1(J+1,n-1))))*vr(J+1,n-1)+dt*beta*ur(J+1,n-1)*(vr(J+1,n-1)+vl(J+1,n-1))-dt*alpha*vr(J+1,n-1);
        %peridic BC for right moving of infected(j=1)
        vr(1,n)=vr(1,n-1)-0.5*mu2*(vr(1,n-1)-vr(J,n-1))+dt*lambdav2*(0.5+0.5*tanh(1+(Z1(1,n-1)+ZZ1(1,n-1))))*vl(1,n-1)-dt*lambdav1*(0.5+0.5*tanh(1+(U1(1,n-1)+UU1(1,n-1))))*vr(1,n-1)+dt*beta*ur(1,n-1)*(vr(1,n-1)+vl(1,n-1))-dt*alpha*vr(1,n-1);
        %peridic BC for left moving of infected(j=1)
        vl(1,n)=vl(1,n-1)+0.5*mu2*(vl(2,n-1)-vl(1,n-1))+dt*lambdav1*(0.5+0.5*tanh(1+(U1(1,n-1)+UU1(1,n-1))))*vr(1,n-1)-dt*lambdav2*(0.5*+0.5*tanh(1+(Z1(1,n-1)+ZZ1(1,n-1))))*vl(1,n-1)+dt*beta*ul(1,n-1)*(vr(1,n-1)+vl(1,n-1))-dt*alpha*vl(1,n-1);
        %peridic BC for left moving of infected(j=J+1)
        vl(J+1,n)=vl(J+1,n-1)+0.5*mu2*(vl(1,n-1)-vl(J+1,n-1))+dt*lambdav1*(0.5+0.5*tanh(1+(U1(J+1,n-1)+UU1(J+1,n-1))))*vr(J+1,n-1)-dt*lambdav2*(0.5*+0.5*tanh(1+(Z1(J+1,n-1)+ZZ1(J+1,n-1))))*vl(J+1,n-1)+dt*beta*ul(J+1,n-1)*(vr(J+1,n-1)+vl(J+1,n-1))-dt*alpha*vl(J+1,n-1);
    end
    for j=1:J+1
        Sr(j)=ur(j,n);
        Sl(j)=ul(j,n);
        Il(j)=vl(j,n);
        Ir(j)=ur(j,n);
    end
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%       
    %calculate the analytical solution 
    for j=1:J+1
        xj=xl+(j-1)*dx;
        u_ex(j,n)=exp(-c*(xj-au*t-0.5)^2);
    end
end 
figure
ss=surf(T,X,ur+ul);
set(ss,'edgecolor','none');
xlabel('t','FontSize',28);
ylabel('x','FontSize',28);
title('u^++u^-','FontSize',28);
set(gca,'Fontsize',28);
view(2)
%%%%%%%%%%%%

Answer 1

[Florian Rössing]

The code tells you that the error is at line 125, which is here:

if ((i+k-J)>=1)
  sum=sum+2*KU0*y1((i+k)-(J+1)); %< the problem ist that you check (i+k-J)>=1 instead of >1
  sum1=sum1+2*KU0*y2((i+k)-(J+1));
  sum2=sum2+2*KV0*F1((i+k)-(J+1));         
  sum3=sum3+2*KV0*F2((i+k)-(J+1));
end

If i+k-J = 1 then (i+k)-(J+1) is 0, which is not a valid index.

Your code has more flaws after that. I suggest you use breakpoints to identify those and fix them one by one.

[lulu]

I appreciate it, I delete an equal (=) in ((i+k-J)>=1) to be ((i+k-J)>1) and I avoid the error but I faced the following error:

Index exceeds the number of array elements. Index must not exceed 1.

Error in trych5A (line 131)

I(i) = ds/2*(2*KU(ds*(J+1))*2*y1(i)+sum+2*KU(ds*(J+1)));

[Florian Rössing]

Like I said, you have more errors. I suggest you learn to debug that by yourself, at last it is your problem and debugging is a useful skill.

Some practice tipps from me:

• Read Error Messages
• Use break points, at the breakpoints check the variables that cause the error, e.g. compare values and sizes with what you would expect
• Try to reproduce errors by building minimal examples, this gives better understanding of how your code works
• Test your code frequently when adding new lines, to ensure that it still works. Debugging only a few lines is easier than debugging a 100 line script

[lulu]

Thank you, I use it. But I could not solve the problem. If anyone has an idea, please help. Thank you

Answer 2

[Image Analyst]

See the FAQ:

https://matlab.fandom.com/wiki/FAQ#%22Subscript_indices_must_either_be_real_positive_integers_or_logicals.%22

Answer 3

[Walter Roberson]

for ii=1:J+1
  Sr =     7.5 + 0.001*(1+sin(X*ii));
  Sl =     7.5 + 0.001*(1+sin(X*ii));
  Ir =     0.0 + 0.001*(1+sin(X*ii));  %initial conditions of infected
  Il =     0.0 + 0.001*(1+sin(X*ii));
end

You are overwriting those variables within the loop, so the result is the same as if you had only done the last iteration. The variables end up as scalars. That causes y1 to become a scalar later.