Use of syms function in 4th order runge kutta method

i have this initial code that asks for user input

but when i run it, it displays an error that says:

The following error occurred converting from sym to double:

Unable to convert expression containing symbolic variables into double

array. Apply 'subs' function first to substitute values for variables.

Error in RK4_try (line 31)

y(i+1) = y(i) + h*((1/6)*k_1+(2/6)*k_2+(2/6)*k_3+(1/6)*k_4);

at which parrt of the code should i be putting the subs function in?

syms x y

%allows values to be printed at an external txt fie
fid=fopen('RK4out.txt','w');

%user input of desired function and values
f = input('Input function dy/dx: ');
a = input('Input lower boundary value, a: ');
b = input('Input upper boundary value, b: ');
h = input('Input step-size, h: ');
c = input('Input initial condition, y(0): ');

%sets number of values of x between a and b with step size h
x = a:h:b;
y = zeros(1, numel(x));

%change value of initial condition y(0) as needed
y(1)= c; %set as y(1) since i values start at 1; y(1) is the same as y(a)

f_xy = @(x,y) f;
%column titles for the table of values
fprintf(fid,'%7s %7s %7s %7s %7s %7s %7s \n','i','x(i)','k1','k2','k3','k4','y(i)');

%computation loop
for i=1:1:(numel(x)-1)
    k_1 = f_xy(x(i),y(i));
    k_2 = f_xy(x(i)+0.5*h,y(i)+0.5*h*k_1);
    k_3 = f_xy(x(i)+0.5*h,y(i)+0.5*h*k_2);
    k_4 = f_xy(x(i)+h,y(i)+k_3*h);
    
    %main 4th order runge kutta equation
    y(i+1) = y(i) + h*((1/6)*k_1+(2/6)*k_2+(2/6)*k_3+(1/6)*k_4);
    
    %prints computed values on the table
    fprintf(fid,'%7d %7.2f %7.3f %7.3f',i, x(i), k_1, k_2);
    fprintf(fid,' %7.3f %7.3f %7.3f \n', k_3, k_4, y(i));
end

fclose(fid);

%solution plot
plot(x,y, '--ok');

%prints the content of the txt file on the command window
type RK4out.txt

Answer 1

[Walter Roberson]

f_xy = @(x,y) f;

That does not take the values passed in and evaluate f substituting them for the variables of the same name.

You should use

f_xy = matlabFunction(f, 'vars', [x, y])

[Sam]

i tried putting that in but then it gave me this error:

Error using sym/matlabFunction>getOptions (line 656)

The value of 'Vars' is invalid. 'Vars' value must be a character

vector, a 1-dimensional cell array of character vectors, a

1-dimensional cell array of symbolic variables or arrays of symbolic

variables, or an array of symbolic variables.

Error in sym/matlabFunction (line 154)

opts = getOptions(args);

Error in RK4_try (line 19)

f_xy = matlabFunction(f, 'vars', [x,y]);

[VBBV]

@Sam use a cell array

syms x y

%allows values to be printed at an external txt fie
%fid=fopen('RK4out.txt','w');

%user input of desired function and values
f = x+y^2; %input('Input function dy/dx: ');
a = 0; %input('Input lower boundary value, a: ');
b = 1; %input('Input upper boundary value, b: ');
h = 0.1;%input('Input step-size, h: ');
c = 0; %input('Input initial condition, y(0): ');

%sets number of values of x between a and b with step size h
x = a:h:b;
y = zeros(1, numel(x));

%change value of initial condition y(0) as needed
y(1)= c; %set as y(1) since i values start at 1; y(1) is the same as y(a)

f_xy = matlabFunction(f, 'Vars', {'x', 'y'}) % use a cell array 

f_xy = function_handle with value:
    @(x,y)x+y.^2

%column titles for the table of values
%fprintf(fid,'%7s %7s %7s %7s %7s %7s %7s \n','i','x(i)','k1','k2','k3','k4','y(i)');

%computation loop
for i=1:1:(numel(x)-1)
    k_1 = f_xy(x(i),y(i));
    k_2 = f_xy(x(i)+0.5*h,y(i)+0.5*h*k_1);
    k_3 = f_xy(x(i)+0.5*h,y(i)+0.5*h*k_2);
    k_4 = f_xy(x(i)+h,y(i)+k_3*h);
    
    %main 4th order runge kutta equation
    y(i+1) = y(i) + h*((1/6)*k_1+(2/6)*k_2+(2/6)*k_3+(1/6)*k_4);
    
    %prints computed values on the table
    %fprintf(fid,'%7d %7.2f %7.3f %7.3f',i, x(i), k_1, k_2);
    %fprintf(fid,' %7.3f %7.3f %7.3f \n', k_3, k_4, y(i));
end

%fclose(fid);

%solution plot
plot(x,y, '--ok');

%prints the content of the txt file on the command window
%type RK4out.txt