Error using plot for Fourier series

This is not plotting. I tried applying fplot and plot and neither will work. I have assigned t so im not sure why I keep getting the error:

"Error using plot

Data must be numeric, datetime, duration or an array convertible to double.

Error in Fourier_example_3 (line 48)

plot(x,F3, 'b' )"

This is my code:

% Fourier Series 
clear all 
syms x k L t
c = 1
f1(x) = x;
f2(x) = L-x;
f1 = simplify(f1);
f2 = simplify(f2);
%Solving for Bn
b(k) = (2/L)*int(f1*sin(k*pi*x/L),[0,L/2]);
b1(k) = (2/L)*int(f2*sin(k*pi*x/L),[L/2,L]);
Bn(k) = b1 + b; 
Bn = simplify(Bn);
N=100;
x = linspace(-L+0.000001,L,N);
t = [0 50 100 200];
for i = 1:1:N
    F = Bn.*sin(pi.*x./L).*exp((-(c.*(pi.^2))/L.^2).*0);
end 
for i = 1:1:N
    F1 = Bn.*sin(pi.*x./L).*exp((-(c.*(pi.^2))/L.^2).*50);
end 
for i = 1:1:N
    F2 = Bn.*sin(pi.*x./L).*exp((-(c.*(pi.^2))/L.^2).*100);
end 
for i = 1:1:N
    F3 = Bn.*sin(pi.*x./L).*exp((-(c.*(pi.^2))/L.^2).*200);
end 
plot(x,F3, 'b' )
plot(x,F,'--r') 
plot(x,F1,'--p') 
plot(x,F2,'-r')
xlabel('x')
ylabel('y')
legend('f','F(x) N=10', 'F(x) N=100','F(x) N=500','location','best')
grid on 
hold off

Answer 1

[Star Strider]

The fplot function is usually best for symbolic functions.

I am not certain what you want to plot.

Try this —

syms x k L t
c = 1;
L = 80;
f1(x) = x;
f2(x) = L-x;
f1 = simplify(f1);
f2 = simplify(f2);
%Solving for Bn
b(k) = (2/L)*int(f1*sin(k*pi*x/L),[0,L/2]);
b1(k) = (2/L)*int(f2*sin(k*pi*x/L),[L/2,L]);
Bn(k) = b1 + b; 
Bn = simplify(Bn)

Bn(k) = 

figure
fplot(Bn,[-L L])
grid
xlabel('k')
ylabel('Bn(k)')

.

[Tashanda Rayne]

I tried fplot and it still is giving me an error :

syms x k L t
c = 1;
f1(x) = x;
f2(x) = L-x;
f1_simplified = simplify(f1);
f2_simplified = simplify(f2);
%Solving for Bn
b(x) = (2/L)*int(f1_simplified*sin(k*pi*x/L),[0,L/2]);
b1(x) = (2/L)*int(f2_simplified*sin(k*pi*x/L),[L/2,L]);
Bn(x) = b1 + b;
Bn_simplified = simplify(Bn);
N = 100;
x = linspace(-pi,pi,N);
t = [0;0.1;0.5;2];
F = zeros(N, 1);
F1 = zeros(N, 1);
F2 = zeros(N, 1);
F3 = zeros(N, 1);
for i = 1:N
    F = Bn_simplified.*sin(pi.*x./L).*exp((-(c.*(pi.^2))/L.^2).*0);
end
for i = 1:N
    F1 = Bn_simplified.*sin(pi.*x./L).*exp((-(c.*(pi.^2))/L.^2).*50);
end
for i = 1:N
    F2 = Bn_simplified.*sin(pi.*x./L).*exp((-(c.*(pi.^2))/L.^2).*100);
end
for i = 1:N
    F3 = Bn_simplified.*sin(pi.*x./L).*exp((-(c.*(pi.^2))/L.^2).*200);
end
hold on

fplot(F , [-L,L])

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

Error in fplot>@(f1,f2)singleFplot(cax,{f1,f2},limits,extraOpts,args) (line 208)
hObj = cellfun(@(f1,f2) singleFplot(cax,{f1,f2},limits,extraOpts,args),fn{1},fn{2},'UniformOutput',false);

Error in fplot>vectorizeFplot (line 208)
hObj = cellfun(@(f1,f2) singleFplot(cax,{f1,f2},limits,extraOpts,args),fn{1},fn{2},'UniformOutput',false);

Error in fplot (line 166)
hObj = vectorizeFplot(cax,fn,limits,extraOpts,args);

fplot(F1 , [-L,L])
fplot(F2 , [-L,L])
fplot(F3 , [-L,L])
hold off
xlabel('x')
ylabel('y')
legend('f','F(x) N=10', 'F(x) N=100','F(x) N=500','location','best')
grid on

[Torsten]

I don't understand why you loop over i if your F, F1, F2 and F3 don't depend on i.

[Tashanda Rayne]

I am attempting to have this code run for different t and k values. I took k out when the code wasnt working. It now looks like this, my apologies. I don't know how to get the code to run

tried fplot and it still is giving me an error :

syms x k L t

c = 1;

f1(x) = x;

f2(x) = L-x;

f1_simplified = simplify(f1);

f2_simplified = simplify(f2);

%Solving for Bn

b(x) = (2/L)*int(f1_simplified*sin(k*pi*x/L),[0,L/2]);

b1(x) = (2/L)*int(f2_simplified*sin(k*pi*x/L),[L/2,L]);

Bn(x) = b1 + b;

Bn_simplified = simplify(Bn);

N = 100;

x = linspace(-pi,pi,N);

t = [0;0.1;0.5;2];

k = 5

for i = 1:2:k

F = Bn_simplified.*sin(k*pi.*x./L).*exp((-(c.*(pi.^2))/L.^2).*t);

end

hold on

fplot(F , [-L,L])

[Walter Roberson]

x = linspace(-pi,pi,N);

That is a vector.

for i = 1:N
    F = Bn_simplified.*sin(pi.*x./L).*exp((-(c.*(pi.^2))/L.^2).*0);
end

The right hand side involves the vector F, so the left hand side will be a vector.

Each iteration you overwrite all of F, so the result is going to be the last value assigned to it... which is the same as the first value assigned to it.

fplot(F , [-L,L])

F is a vector of symbolic values, so you are asking to fplot() a symbolic vector. That isn't going to work very well.

Answer 2

[Torsten]

I'm not sure what you try to do. Maybe something like this:

clear all 
syms x 

L = 2;
f = piecewise(x<=L/2,x,x>L/2,(L-x));

N = 5;
b = 2/L*int(f*sin((1:N)*pi*x/L),x,[0,L]);

F{1} = 0;
for k = 1:N
  F{k+1} = F{k} + b(k)*sin(pi*k*x/L);
end
hold on
fplot(F,[0 L])
fplot(f,[0 L])
hold off
grid on

[Tashanda Rayne]

This worked but I need to specify the t. The complete equation for

F = Bn_simplified.*sin(k*pi.*x./L).*exp((-(c.*(pi.^2))/L.^2).*t);

[Torsten]

Why not simply multiplying F by the factor ?

syms x 

t = 1;
c = 1;
L = 2;
f = piecewise(x<=L/2,x,x>L/2,(L-x));

N = 5;
b = 2/L*int(f*sin((1:N)*pi*x/L),x,[0,L]);

F{1} = 0;
for k = 1:N
  F{k+1} = F{k} + b(k)*sin(pi*k*x/L)*exp(-c*pi^2/L^2*t);
end

hold on
fplot(F,[0 L])
fplot(f,[0 L])
hold off
grid on