HOW TO FIND THE MODULUS OF THE COMPLEX SERIES

syms x %a
syms t
a=1

a = 1

c=0.1

c = 0.1000

U=zeros(1,2,'sym');
A=zeros(1,2,'sym');
B=zeros(1,2,'sym');
C=zeros(1,2,'sym');
D=zeros(1,2,'sym');
series(x,t)=sym(zeros(1,1))

series(x, t) = 

0

modulus_complex_E=sym(zeros(1,1))

modulus_complex_E = 

0

modulus_exact=sym(zeros(1,1))

modulus_exact = 

0

U(1)=sqrt(-15*c*cosh(sqrt(0.1)*((x-c*t)/3)))*sqrt(-15*c*cosh(sqrt(0.1)*((x-c*t)/3)))

U = 

%%%%%%%%%%%%%%%%
for i=1:2
    A(1)=0;
    B(1)=0;
    C(1)=0;
    D(1)=0;
    for j=1:i
        for k=1:j
            A(1)=A(1)+U(k)*U(j-k+1)*diff(U(i-j+1),x,1);
            B(1)=B(1)+diff(U(k),x,1)*diff(U(j-k+1),x,1)*diff(U(i-j+1),x,1);
            C(1)=C(1)+U(k)*U(j-k+1)*diff(U(i-j+1),x,3);
            D(1)=D(1)+U(k)*diff(U(j-k+1),x,1)*diff(U(i-j+1),x,2);
        end
    end
    U(i+1)=simplify((gamma(a*(i-1)+1)/gamma(a*i+1))*(0.3*A(1)-6*B(1)-3*C(1)-18*D(1)));
end
%U
for i=1:3
    series(x,t)=series(x,t)+U(i)*(power(t,i-1));
end
%series
modulus_complex=abs(series)

modulus_complex(x, t) = 

modulus_complex_E=sqrt(-15*c*(cosh(sqrt(0.1)*(1/3)*(x-c*t)))^2)

modulus_complex_E = 

modulus_exact=abs(modulus_complex_E)

modulus_exact = 

% format long 
x=0:0.05:1;
t=0:0.05:1;
row=0

row = 0

C=zeros(1)

C = 0

C1=zeros(1)

C1 = 0

% exact=zeros(1)
modulus_exact=zeros(1)

modulus_exact = 0

for i=1:length(x)
    row=row+1;
    col=0;
    for j=1:length(t)
        col=col+1;
        C(row,col)=modulus_complex(x(row),t(col));
        C1(row,col)=modulus_exact(x(row),t(col));
        % C(row,col)=series(x(i),t(j));
        %exact(row,col)=sqrt(-15*c*cosh((sqrt(0.1)*(x(i)-c*t(j)))/3)*cosh((sqrt(0.1)*(x(i)-c*t(j)))/3));
        % abs_error(row,col)=abs(C(row,col)-C1(row, col));
    end
end

Index in position 1 is invalid. Array indices must be positive integers or logical values.

% C
% exact
% abs_erro

WHEN I COMPLE IT I GOT THE FOLLOWING ERROR :

Index in position 1 is invalid. Array indices must be positive integers or logical values.

Answer 1

[Walter Roberson]

Although modulus_complex is a function, modulus_exact is not a function, so modulus_exact(x(row),t(col)) is attempting to index the scalar symbol modulus_exact . You need

modulus_complex_E(x,t)=sqrt(-15*c*(cosh(sqrt(0.1)*(1/3)*(x-c*t)))^2)

Your code follows that with

modulus_exact=abs(modulus_complex_E)

which will work fine to create a function of x and t.

However, just before the loop you have

modulus_exact=zeros(1)

which overwrites modulus_exact