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Results tagged with reference-request
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user 88548
This tag is for requests for books, online resources, etc. that deal with the Mathematica system and its applications. This tag is also for asking references for algorithms used within Mathematica.
2
votes
1
answer
89
views
Using Mathematica Confirm Bessel's Inequality
I am working on the following Fourier series problem
f[x_] = Which[-1 < x < 0, 0, 0 < x < 1, x^2]
Plot[f[x], {x, -1, 1}]
a[n_] := (2/L)*Integrate[f[x]*Cos[2 n*Pi*x/L], {x, -L/2, L/2}]
a[0] := (1/L)* …
3
votes
1
answer
274
views
Euler's Method for system of differential equation with more than two functions
According to what I have read, the first formula is the classical Euler method and the second is the improved Euler method for second-order equations.
Method A: accuracy of order h
S[a_, b_, h_, N_] …
1
vote
1
answer
127
views
Understanding the calculation of the periodic function $f(x)=x-x^3, \quad -1<x<1$
It is given the following periodic function
$$f(x)=x-x^3, \quad -1<x<1$$
This is an odd function, so the coefficients $a_n,a_0$ of the Fourier Series are zero.
Usually, I face function with two branch …
3
votes
Accepted
Euler's Method for system of differential equation with more than two functions
This works but it is not as accurate as the NDSolve result
α=0.9;
β=0.2;
γ=1.2;
f[x_,y_,z_]:=z+(y-α)*x
g[x_,y_,z_]:=1-β*y-x^2
p[x_,y_,z_]:=-x-γ*z
Q[a_,b_,c_,h_,N_]:=(u[0]=a;v[0]=b;w[0]=c;
Do[{u[n+ …