Solve IVP with Taylor method of order

I wanna implement this into a code.

My code is followed by :

• syms x y(x)
• f = y(x) - x^3 + x + 1
• df = diff(f, x)
• f = subs(df, diff(y(x), x), f)

and it gives OUTPUT

• f = x + y(x) - 3*x^2 - x^3 + 2

What I am trying to do is change y(x) (symfun) to new y variable

so that I can use the function of f(x,y) = x + y - 3*x^2 - x^3 + 2; to plug f(a,b) into x and y variable.

[Torsten]

So what's your numerical method to solve the IVP ?

y_(n+1) = y_n + dx*y_n' + dx^2/2 * y_n'' 

?

Answer 1

[Walter Roberson]

https://www.mathworks.com/matlabcentral/answers/1746100-whole-derivation-of-two-variable-differential-function#comment_2229660 already shows you how to change to a different variable yx

If you really really need it to be in terms of y and no other name will do then you can follow with

syms y
subs(sol, yx, y)

The "syms y" will destroy the association between the name y and the symbolic function y(x) allowing a substitution as a name instead of a function.

There are ways to do this without using a temporary variable name such as the "yx" that I showed.

But I already showed you exactly how to substitute in numeric values.

[Minjae Cho]

Thanks a lot!

I was gonna do it recursively for Taylor method of order.

It was a lot of help thanks!