taylor series method expansion

I am using the following code for taylor series

function [T,Y] = taylor(f,a,b,ya,m)
h = (b - a)/m;
T = zeros(1,m+1);
Y = zeros(1,m+1);
T(1) = a;
Y(1) = ya;

for j=1:m
  tj = T(j);
  yj = Y(j);
  D = feval('df',tj,yj);
  Y(j+1) = yj + h*(D(1)+h*(D(2)/2+h*(D(3)/6+h*D(4)/24)));
  T(j+1) = a + h*j;
end

At command prompt i am giving the values as follows and getting error

>> syms x y;
>> f=4*x^3+1
f =
4*x^3 + 1
>> taylor(f,0,1,1.5,4)
Error using sym/taylor (line 99)
The value of 'x' is invalid. It must satisfy the function: @(x)isvector(x)&&isAllVars(x).

[PJS KUMAR]

> f
f =
  function_handle with value:
    @(x,y)x^2+y^2
>> taylor2(f,0,1,1.5,5)
Error using feval
Undefined function 'df' for input arguments of type 'double'.
Error in taylor2 (line 11)
  D = feval('df',tj,yj);

Kindly suggest me how to get rid of this problem

[Walter Roberson]

... create df.m ?

There is no Mathworks provided function named df

[PJS KUMAR]

can u suggest how to create df.m for a function

[Walter Roberson]

Use a function line,

function result = df(t, y)
   ... do appropriate calculation here
   result = appropriate value to return

[PJS KUMAR]

my intention to use 'df' is to find derivative of 'f' and evaluate it at tj and yj. Suggest me alternative code for the following statement in the above program. D = feval('df',tj,yj);

[Torsten]

function D = df(t,y)
D(1) = 12*t^2;
D(2) = 24*t;
D(3) = 24;
D(4) = 0;
end

[Walter Roberson]

I am not clear what the parameters of your taylor represent so I do understand the meaning of t and y being passed to df.

I can say you should probably not be mixing feval with syms.

[PJS KUMAR]

can we use 'diff' function to assign derivatives to D(1), D(2), D(3) etc.

[Walter Roberson]

Well you could if you had a variable name to take the derivative with respect to, and you had some reason for D(1) being different from D(2), D(3) etc.

Answer 1

[Walter Roberson]

You are somehow invoking the symbolic toolbox taylor routine instead of your own. Make sure that you match file name with function name and that your path is correct to prioritize your own function.