Error: Unable to perform assignment because the left and right sides have a different number of elements.

I'm trying 2d velocity equation in tridigonal system. I stuck in the rhs of tridigonal equation. I got error "Unable to perform assignment because the left and right sides have a different number of elements."

when i use this equation i couldn't rectify my programme. I'm taking this equation in three multiple equation for top and bottom boundary and interior nodes.

ymax=20; m=80; dy=ymax/m; %y=dy:dy:ymax;        %'i'th row
xmax=1; n=20; dx=xmax/n;                        %'j'th column   
tmax=100; nt=500; dt=tmax/nt; t=0:dt:tmax;      
tol=1e-2;
max_Iteration=1;
UWALL=ones(m,nt); %INITIAL VALUE
UOLD=zeros(m,nt);
UNEW=0;  %BOUNDARY VALUE
VOLD=zeros(m,nt);
CNEW=0;COLD=CNEW*ones(m,nt);CWALL=ones(1,length(t));
TNEW=0;TOLD=TNEW*ones(m,nt);TWALL=ones(1,length(t));
A=zeros([1,m]);
B=A;
C=A;
D=A;
T=TOLD; U=UOLD;
%============CALCULATE INTEGRAL USING SIMPHONS RULE==============% 
F = @(ymax) ymax;
a = 0;
b = 20;
N1 = 80;             
h = b-a/N1;
s = 0;
for w = 0:20
    if w == 0 || w == 20
        p = 1;
    elseif mod(w,2) ~= 0
        p = 4;
    else
        p = 2;
    end
    X = a+w*h;
    S = s+p*F(ymax);
end
I = h/3*S; 
%================================================%
while max_Iteration>tol
   for j=2:nt
        for i=2:m-1
            if i==2 
                D(i)=UOLD(i,j)-(dt*UOLD(i,j)*(-U(i,j-1)+UOLD(i,j)-UOLD(i,j-1)/2*dx))+(dt*(UWALL(j)-2*UOLD(i,j)+UOLD(i-1,j)/2*dy^2))+(dt*E2*(gr^(-1/4)*cos(phi)*I*diff(TWALL(j),xmax)+(1/2)*sin(phi)*(TWALL(j)+TOLD(i,j))))-(dt*VOLD(i,j)*(UOLD(i-1,j)-UWALL(j)/4*dy))-(dt*(UWALL(j)/2*dy^2));
            elseif i==m-1
                D(i)=UOLD(i,j)-(dt*UOLD(i,j)*(-U(i,j-1)+UOLD(i,j)-UOLD(i,j-1)/2*dx))+(dt*(UOLD(i+1,j)-2*UOLD(i,j)+UNEW/2*dy^2))+(dt*E2*(gr^(-1/4)*cos(phi)*I*diff(TNEW,xmax)+(1/2)*sin(phi)*(TNEW+TOLD(i,j))))-(dt*VOLD(i,j)*(UNEW-UOLD(i+1,j)/4*dy))-(dt*(UNEW/2*dy^2));
            else
                D(i)=UOLD(i,j)-(dt*UOLD(i,j)*(-U(i,j-1)+UOLD(i,j)-UOLD(i,j-1)/2*dx))+(dt*(UOLD(i+1,j)-2*UOLD(i,j)+UOLD(i-1,j)/(2*dy^2)))-(dt*VOLD(i,j)*(UOLD(i-1,j)-UOLD(i+1,j)/4*dy))+(dt*E2*(gr^(-1/4)*cos(phi)*I*diff(T,xmax)+(1/2)*sin(phi)*(T+TOLD(i,j))));
            end
        end
        max_Iteration=max_difference;
    end
end

Unrecognized function or variable 'E2'.

Kindly assist me to finish well.

[Walter Roberson]

E2 and gr (and possibly others) are not defined.

[Nathi]

@Walter Roberson Please neglect E2 and the value of gr =10^6 and phi =45.

Answer 1

[Walter Roberson]

TNEW=0;TOLD=TNEW*ones(m,nt);TWALL=ones(1,length(t));

TWALL is numeric.

                
D(i)=UOLD(i,j)-(dt*UOLD(i,j)*(-U(i,j-1)+UOLD(i,j)-UOLD(i,j-1)/2*dx))+(dt*(UWALL(j)-2*UOLD(i,j)+UOLD(i-1,j)/2*dy^2))+(dt*E2*(gr^(-1/4)*cos(phi)*I*diff(TWALL(j),xmax)+(1/2)*sin(phi)*(TWALL(j)+TOLD(i,j))))-(dt*VOLD(i,j)*(UOLD(i-1,j)-UWALL(j)/4*dy))-(dt*(UWALL(j)/2*dy^2));

diff(TWALL(j),xmax) with xmax == 1, is the "first" numeric difference of TWALL(j) . diff(X,1) is equivalent to X(2:end)-X(1) for vector X. But TWALL(j) is a scalar, and the 2:end of a scalar is empty, so diff(TWALL(j),1) is going to be empty. That "empty" contaminates everything else in the calculation; the right hand side is going to be empty.

diff() is only derivative when you are working with sym or symfun -- or for the case where the first parameter is an anonymous function and the second parameter is a symbolic variable

[Nathi]

@Walter Roberson You exactly got where i went wrong. I didn't approach this the right way. we have to notice in this term have partial derivative of integrals.

For that purpose, i'm using diff(TWALL(j),xmax). According to me, it is differentiate w.r.to x . but we notice one thing in the term i.e., 'T' term is into the integral. so, we can use TWALL is a function of integral w.r.to Y. If we use T is a function of integral, then we have to modify the integration part using simphons rule.

i.e.,

%============CALCULATE INTEGRAL USING SIMPHONS RULE==============% 
F = @(ymax) TWALL;   i'm using TWALL instead of ymax
a = 0;
b = 20;
N1 = 80;             
h = b-a/N1;
s = 0;
for w = 0:20
    if w == 0 || w == 20
        p = 1;
    elseif mod(w,2) ~= 0
        p = 4;
    else
        p = 2;
    end
    X = a+w*h;
    S = s+p*F(ymax);
end
I = h/3*S; 

And i'm changing this equation [ diff(I,xmax) ] instead of [ I*diff(TWALL, xmax) ]

 D(i)=UOLD(i,j)-(dt*UOLD(i,j)*(-U(i,j-1)+UOLD(i,j)-UOLD(i,j-1)/2*dx))+(dt*(UWALL(j)-2*UOLD(i,j)+UOLD(i-1,j)/2*dy^2))+(dt*(gr^(-1/4)*cos(phi)*diff(I,xmax)+(1/2)*sin(phi)*(TWALL(j)+TOLD(i,j))))-(dt*VOLD(i,j)*(UOLD(i-1,j)-UWALL(j)/4*dy))-(dt*(UWALL(j)/2*dy^2));

but i got the same error :"Unable to perform assignment because the left and right sides have a different number of elements". I really stuck in this part. how to approach this integrodifferential and include it in my equation ?

please suggest and give some idea about this.