MATLAB: Symbolic multivariable Taylor series first order approximation

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Hi,

Is there any way to find symbolic multivariable Taylor series first order approximation of a 1st order ODE using MATLAB ??

Thanks in advance

Best Answer

You can use mupad for this. Suppose your ODE is dot(.)=f(x,y....) and you want to expand along(x0,yo,....) and n is the order upto which you want to truncate, then the command in mupad is

mtaylor(f, [x = x0, y = y0, ...],n)

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MATLAB: Taylor’s Approximation playing up

The result is mathematically correct, but the display could be simplified. 1301357606610903 / 4722366482869645213696 equals 1 / 3628800. Now it matters, what exactly your question is. Do you want to know how to simplify the output or why the values are displayed in this way?

Maybe simplifyFraction helps. ([EDITED] Nope, it does not.)

Move the factorial out of the symbolic part to the numerical part:

FuncApprox = FuncApprox + f_derrived(a) * (x - a)^i / factorial(i)

This works also, when i! exceeds flintmax.

[EDITED] Another solution:

FuncApprox = FuncApprox + (f_derrived(a) / factorial(sym(i))) * (x - a)^i;

MATLAB: How to write f”’ + f’f” = 0 in matlab

YOu can write first,second and third derivative like below:

df = diff(f,t) ;   %f'
d2f = diff(f,t,t) ; % f''
d3f = diff(f,t,t,t) ; % f'''

Check below option also:

syms f(t)  
df = diff(f,t) ;
d2f = diff(df,t) ;
d3f = diff(d2f,t) ;
ode = d3f+df*d2f == 0
dsolve(ode)

Best Answer

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MATLAB: Taylor’s Approximation playing up

MATLAB: How to write f”’ + f’f” = 0 in matlab

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