Iterative method-Problems with array of symbolic functions

Tommaso Franzini

2019 12 14

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Hello everyone.

I'm trying to write a code for an iterative method, using symbolic functions, but I have this error when I try to plot:

  Error using fplot>singleFplot (line 240). Input must be a function or functions of a single variable.  

I think that the problem can be related on the way I am using the sym arrays to store these functions or in the way I am calculating the convolution of sym functions (it is the only part of the code where i use a function of more than 1 variable).

Do you know if these is a more effective way to write the convolution?

Here is the code:

N=5;
k=0.01;
syms x y;
    E = sym(zeros(N,1));
    L = sym(zeros(N,1)); 
    F = sym(zeros(N,1));
f(x,y)=-sqrt(3)/pi*sinh(2*x-2*y)/sinh(3*x-3*y);
A=2*log(2/k);
E(1)=k*cosh(y);
figure(); hold on
    for i=1:3
        L(i)=log(1+exp(-E(i)));
        F(i)=int(f(x,y)*L(i),y,-A,A); %convolution
        E(i+1)=E(1)+F(i);
        if i==3
            fplot(L(i),[-10,10]);
            break;
        else
            continue;
        end
    end
  hold off
  

Thank you very much.

--------------------EDIT-------------------------

I've changed the method to perform the convolution, and now I don't have errors anymore.

If I plot L(1) (see below) no problems, but when I try to plot L(i) (for example L(3)) I have an empty graph. Maybe there are still some problems when I try to fill the L array?

  N=5;
k=0.01;
syms x y w;
    E = sym(zeros(N,1));
    L = sym(zeros(N,1)); 
f(x)=-sqrt(3)/pi*sinh(2*x)/sinh(3*x);
g(w)=fourier(f);
A=2*log(2/k);
E(1)=k*cosh(x);
figure(); hold on
    for i=1:3
        L(i)=log(1+exp(-E(i)));
        h(w)=fourier(L(i));
        l(w)=g*h;
        s(x)=ifourier(l);
        E(i+1)=k*cosh(x)+s;
        if i==3
            %fplot(L(1),[-10,10]); %This works 
            fplot(L(i),[-10,10]); %Doesn't work
            break;
        else
            continue;
        end
    end
  hold off

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Star Strider 2019-12-14

The ‘L’ function is a function of x and y. Trying to plot it with fplot throws an error reflecting that, and it is seenttially impossible to plot it with fsurf.

It would likely be much more efficient to do this numerically and avoid the Symbolic Math Toolbox.

I cannot figure out from your code what you want to do.

Tommaso Franzini 2019-12-14

Thank you very much for your quick answer.

I tried but I think it's too complicated trying to manipulate these functions numerically (for me). I've edited the post, changing a few things in the code: now it gives no error but there are still some problems since it doesn't plot properly.

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