How to use 'for' loop for time loop?

Here, 'for'loop in the index 'j' not satisfied the first three D equatiions. if I plot D, then I got first values only and all other values zero. but I want smooth curve. how to use For loop in the j th iteration to satisfy all six multiple eqaution?

clc
clear all
%======================SPACEGRID====================================%
ymax=14; m=56; dy=ymax/m; y=dy:dy:ymax;      %'i'th row
xmax=1; n=20;  dx=xmax/n; x=dx:dx:xmax;      %'j'th column   
x1=dx:xmax;
%=====================TIMEGRID======================================%
tmax=100; nt=500; dt=tmax/nt; t=dt:dt:tmax;      % time at 'j'
UOLD=zeros(m,nt); VOLD=zeros(m,nt); 
TNEW=0;TOLD=TNEW*ones(m,nt);TWALL=ones(1,length(t));
D=zeros([1,m]); 
T=TOLD; 
for j=1:nt
 if j==1
      for i=1:m
          if i==1
              D(i)=-dt*UOLD(i,j)*(-TNEW+TOLD(i,j)-TNEW)/(2*dx)-dt*VOLD(i,j)*(TOLD(i+1,j)-TWALL(j)+TOLD(i,j))/(4*dy)-(-dt)*VOLD(i,j)/(4*dy)+dt*(TWALL(j)-2*TOLD(i,j)+TOLD(i+1,j))/(2*dy^2)-dt*TWALL(j)/2*dy^2;
          elseif i==m
              D(i)=-dt*UOLD(i,j)*(-TNEW+TOLD(i,j)-TNEW)/(2*dx)-dt*VOLD(i,j)*(TNEW-TOLD(i-1,j)-TOLD(i,j))/(4*dy)-dt*VOLD(i,j)/(4*dy)+dt*(TOLD(i-1,j)-2*TOLD(i,j)+TNEW)/(2*dy^2)-dt*TNEW/2*dy^2;
          else
              D(i)=-dt*UOLD(i,j)*(-TNEW+TOLD(i,j)-TNEW)/(2*dx)-dt*VOLD(i,j)*(TOLD(i+1,j)-TOLD(i-1,j)+TOLD(i,j))/(4*dy)+dt*(TOLD(i-1,j)-2*TOLD(i,j)+TOLD(i+1,j))/(2*dy^2);
          end
      end
else
      for i=1:m
          if i==1
              D(i)=-dt*UOLD(i,j)*(-T(i,j-1)+TOLD(i,j)-TOLD(i,j-1))/(2*dx)-dt*VOLD(i,j)*(TOLD(i+1,j)-TWALL(j)+TOLD(i,j))/(4*dy)-(-dt)*VOLD(i,j)/(4*dy)+dt*(TWALL(j)-2*TOLD(i,j)+TOLD(i+1,j))/(2*dy^2)-dt*TWALL(j)/2*dy^2;
          elseif i==m
              D(i)=-dt*UOLD(i,j)*(-T(i,j-1)+TOLD(i,j)-TOLD(i,j-1))/(2*dx)-dt*VOLD(i,j)*(TNEW-TOLD(i-1,j)+TOLD(i,j))/(4*dy)-dt*VOLD(i,j)/(4*dy)+dt*(TOLD(i-1,j)-2*TOLD(i,j)+TNEW)/(2*dy^2)-dt*TNEW/2*dy^2;
          else
              D(i)=-dt*UOLD(i,j)*(-T(i,j-1)+TOLD(i,j)-TOLD(i,j-1))/(2*dx)-dt*VOLD(i,j)*(TOLD(i+1,j)-TOLD(i-1,j)+TOLD(i,j))/(4*dy)+dt*(TOLD(i-1,j)-2*TOLD(i,j)+TOLD(i+1,j))/(2*dy^2);
          end
      end
 end
end
plot(D)

Answer 1

[Torsten]

Your code is equivalent with the code below because in D(i), you overwrite all the results you got for j < nt.

All arrays UOLD, VOLD, TNEW, TOLD consist of zeros except TWALL. TWALL only influences D(1). So you get D(1) different from 0 and all other array elements of D equal to 0.

clc
clear all
%======================SPACEGRID====================================%
ymax=14; m=56; dy=ymax/m; y=dy:dy:ymax;      %'i'th row
xmax=1; n=20;  dx=xmax/n; x=dx:dx:xmax;      %'j'th column   
x1=dx:xmax;
%=====================TIMEGRID======================================%
tmax=100; nt=500; dt=tmax/nt; t=dt:dt:tmax;      % time at 'j'
UOLD=zeros(m,nt); VOLD=zeros(m,nt); 
TNEW=0;TOLD=TNEW*ones(m,nt);TWALL=ones(1,length(t));
D=zeros([1,m]); 
T=TOLD; 
j = nt;
for i=1:m
    if i==1
        D(i)=-dt*UOLD(i,j)*(-T(i,j-1)+TOLD(i,j)-TOLD(i,j-1))/(2*dx)-dt*VOLD(i,j)*(TOLD(i+1,j)-TWALL(j)+TOLD(i,j))/(4*dy)-(-dt)*VOLD(i,j)/(4*dy)+dt*(TWALL(j)-2*TOLD(i,j)+TOLD(i+1,j))/(2*dy^2)-dt*TWALL(j)/2*dy^2;
    elseif i==m
        D(i)=-dt*UOLD(i,j)*(-T(i,j-1)+TOLD(i,j)-TOLD(i,j-1))/(2*dx)-dt*VOLD(i,j)*(TNEW-TOLD(i-1,j)+TOLD(i,j))/(4*dy)-dt*VOLD(i,j)/(4*dy)+dt*(TOLD(i-1,j)-2*TOLD(i,j)+TNEW)/(2*dy^2)-dt*TNEW/2*dy^2;
    else
        D(i)=-dt*UOLD(i,j)*(-T(i,j-1)+TOLD(i,j)-TOLD(i,j-1))/(2*dx)-dt*VOLD(i,j)*(TOLD(i+1,j)-TOLD(i-1,j)+TOLD(i,j))/(4*dy)+dt*(TOLD(i-1,j)-2*TOLD(i,j)+TOLD(i+1,j))/(2*dy^2);
    end
end
D

D = 1×56

1.5938 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

[Nathi]

@Torsten then what I will do to get values in D. if i change 'j' index using for loop, then it will give values instead of zero. but its not the smooth.