Matlab Picard Method - Assigning existing symfun to a Vector

Question

I am working on a program for the picard method in matlab. This requires multiple iterations over a function being substituted in a to be integrated polynomial.

Now I have an existing polynomial with syms x, which is defined by some vector a:

 for i = 1:degree+1
     polynomial = symfun(polynomial + a(i) *x^(i-1), x);
 end

 syms t;
 y = symfun( zeros(1,maxIterations+1),x);
 y(1) = polynomial;

 for i = 2: maxIterations
   substitute = subs(polynomial, x, y(i-1));
   y(i) = symfun(x0 + int( substitute, t), x);  %for some predefined x0
 end

But it fails when I try to use y(1) = symfun(polynomial,x);, giving me an error:

Invalid indexing or function definition. When defining a function, ensure that the arguments are symbolic variables and the body of the function is a SYM expression. When indexing, the input must be numeric, logical, or ':'.

But as polynomial is just a symfunction, why can't it be assigned to a slot in the vector y? I already tried using feval() and not using symfun() whilst defining, but nothing worked so far.

Complete code:

    %%Input

prompt = 'What is the degree of the polynomial?   \n ';
degree = input(prompt);

a = zeros(degree+1,1);
for i = 1:degree+1
    a(i) = input(['Enter value of coefficient a_' num2str(i-1) ': ']);
end

prompt = 'What is the number of iterations?   \n ';
maxIterations = input(prompt);

prompt = 'What is the value of x0?   \n ';
x0 = input(prompt);

%%Computing Integrated Vector

aInt = [0];
for i = 1:degree+1
    aInt(i+1) = a(i)/(i);
end

fprintf('x0');
for i = 1: degree+1
  fprintf( [' + ' num2str(aInt(i+1)) ' x^' num2str(i)] );
end

fprintf('\n');

syms x;
polynomial = 0;

for i = 1: degree+1

    polynomial = symfun(polynomial + a(i) * x ^(i-1), x);  

end

%Picard Method
syms t;
syms y;
y = symfun( zeros(maxIterations+1,1), x );
y(1) = polynomial;
for i = 2: maxIterations
    substitute = subs(polynomial, x, y(i-1));
    y(i) = symfun(x0 + int( substitute,t ), t);

end

for i = 1:maxIterations
    fprintf(['x_' num2str(i-1) ' = ' y(i), ' \n']);
end

Thanks in advance!

Answer 1

Fixed it! This is the working code. (might still have slights errors in it). The mistake was not properly defining polynomial, as I first had syms(polynomial) which caused the sum of the polynomial to include `polynomial' as a variable. Also fixed some slight other errors considering the picard method such as the definition of y(1).

%%Input

prompt = 'What is the degree of the polynomial?   \n ';
degree = input(prompt);

a = zeros(degree+1,1);
for i = 1:degree+1
    a(i) = input(['Enter value of coefficient a_' num2str(i-1) ': ']);
end

prompt = 'What is the number of iterations?   \n ';
maxIterations = input(prompt);

prompt = 'What is the value of x0?   \n ';
x0 = input(prompt);

%%Computing Integrated Vector

aInt = [0];
for i = 1:degree+1
    aInt(i+1) = a(i)/(i);
end

%%vector print

fprintf('x0');
for i = 1: degree+1
  fprintf( [' + ' num2str(aInt(i+1)) ' x^' num2str(i)] );
end

fprintf('\n');

syms x;
polynomial = 0; 

for i = 1: degree+1

    polynomial = polynomial + symfun(a(i) * x ^(i-1), x);  

end

%Picard Method
syms t;
syms y;
y = sym( 'y', [1 maxIterations] );
y(1) = x0;

for i = 2: maxIterations
    substitute = subs(polynomial, x, y(i-1));
    y(i) = symfun(x0 + int( substitute, t ), t);
end

for i = 1:maxIterations
    fprintf('The iteration y_%d = %s \n',(i-1), y(i))

end

%plot graphs