I am trying to execute the code written below and getting the error given below, help me to fix this error?

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Abhinav 2014-4-30

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评论： Star Strider 2014-5-2

The following error occurred converting from sym to double: Error using mupadmex Error in MuPAD command: DOUBLE cannot convert the input expression into a double array.

If the input expression contains a symbolic variable, use the VPA function instead.

Error in ExampleLoop (line 13) h(i,j) = 10*(((t(i,j)-.1)/.4)^-0.5-1)^.5;

code: clc; clear all; close all;

t = zeros(100,48); t(1,:) = .5;

t(:,1) = 0;

d = zeros(100,48);

k = zeros(100,48);

h = zeros(100,48);

syms t(i,j);

h(i,j) = 10*(((t(i,j)-.1)/.4)^-0.5-1)^.5;

k(i,j) = 10^-8*(t(i,j)-.1)/(.4)*(1-(1-((t(i,j)-.1)/0.4)^2)^.5)^2;

dh_dt(i,j) = diff(h(i,j));

dk_dt(i,j) = diff(k(i,j));

c(i,j) = 1/(dh_dt(i,j));

d(i,j) = k(i,j)/c(i,j);

dd_dt(i,j) = diff(c(i,j));

for i=2:99;

    for j=1:47;
        a = (1-.5*d(i,j)-.5*d(i+1,j));
        b = .5*d(i,j);
        c = .5*d(i+1,j);
        t(i,j+1) = a*t(i,j)+b*t(i-1,j)+c*t(i+1,j)+.5*(k(i+1,j)-k(i-1,j)); 
   end

end

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Star Strider 2014-4-30

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There are a few things wrong that I can see:

Do not use the ‘syms’ statement. You don’t need it. Use nested for loops for ‘i’ and ‘j’ instead.

In this and other statements like it:

dh_dt(i,j) = diff(h(i,j));

you are taking the difference of a single scalar element. That is not possible. (This would not have worked as a symbolic either, because your h matrix was not created as a function of a symbolic variable.)

What do you want to do in your code?

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Abhinav 2014-5-1

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I know the algorithm. But I am having problem implementing in Matlab. Let me explain the algorithm: 1. I have to get theta as a function of x and t. 2. D and K are dependent on theta. 3. Now to solve the problem I will use discret form of above pde.

theta(i,j+1) = a*theta(i,j) + b*theta(i-1,j) + c*theta(i+1,j) + (1/1440)*(k(i+1,j) - k(i-1,j));

 a = (1-(1/1440)*d(i,j)-(1/1440)*d(i+1,j));
 b = (1/1440)*d(i,j);
 c = (1/1440)*d(i+1,j); 
where i and j are space and time coordinates  respectively.
4. as evident in the above equation theta(i,j+1) is function of theta(i,j),theta(i+1,j),theta(i-1,j). By boundary and initial conditions I know theta(1,;) and theta(:,1). So above equation will give value for all possible i ans j's.
I hope algorithm is clear now.
*My problem exactly is:
I Know 'h' as a function of theta and 'd' = k*(derivative of h w.r.t. theta). I differentiated the h as follows:-
syms theta;
h = a function of theta;
diff(h);
*but this way dh/d(theta) is stored as a function of theta, while actually theta is a matrix, i don't know how to give a specific matrix element as input in this case.* _