Numerical method to solves the system of ODE's
Euler Method
def EulerOdeSys(f,c,t):
H=t[1]-t[0]
N=len(t)
M=len(c)
z = np.ones((N, M))
z[0] = c
for i in range(N):
z[i+1]=z[i]+H*f(z[i],t[i])
return z
And \(\mathcal{ Mathematics }\) is supported!
Use $$ to wrap your formulas. For example, $$ e^{i\pi} + 1 = 0 $$ displays \(e^{i\pi} + 1 = 0\)
Multi-line forumlas are supported too.
$ \begin{aligned} & J(w, b) = \frac{1}{m} \sum_{i=1}^{m}L(\hat{y}^{(i)}, y^{(i)})
- \frac{\lambda}{2m} \sum_{l=1}^{L}{||w||}^2F\
& {||w||}^2_F = \sum{i = 1}^{n[l]}\sum_{j = 1}^{n[l-1]}(w_{ij})^2 \end{aligned} $
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And more…Z =
9
$
10
\begin{pmatrix}
11
x_1(t_0)& x_2(t_0)&\cdots& x_{M}(t_0)
12 x_1(t_1)& x_2(t_1)&\cdots& x_{M}(t_1)
13 x_1(t_2)& x_2(t_2)&\cdots& x_{M}(t_2)
14 \vdots& \vdots&\ddots& \vdots
15 x_1(t_{N})& x_2(t_{N})&\cdots& x_{M}(t_{N}) 16 \end{pmatrix} 17 $
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nocomments: trueinto YAML Front Matter. Z = 9 $ 10 \begin{pmatrix} 11 x_1(t_0)& x_2(t_0)&\cdots& x_{M}(t_0)
12 x_1(t_1)& x_2(t_1)&\cdots& x_{M}(t_1)
13 x_1(t_2)& x_2(t_2)&\cdots& x_{M}(t_2)
14 \vdots& \vdots&\ddots& \vdots
15 x_1(t_{N})& x_2(t_{N})&\cdots& x_{M}(t_{N}) 16 \end{pmatrix} 17 $ EasyBook uses upaiyun CDN to make everyone lncluding Chinese visitors feel speedy. You can find it in_includes/footer.htmland change it to your favorite CDN like Google CDN.
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