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Numerical solution of pendulum equation
Accepted answer
2 votes

With the functions $y_1 := f$, $y_2 := f'$, $\pmb{y} := (y_1,y_2)^{\top}$, we obtain an initial-value problem with an autonomous first-order system: $$ \pmb{y}' = \left( \begin{array}{c} y_2\\ -a \sin(...

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Neumann boundary conditions diffusion equations methods of lines
1 votes

It is easy to see that the function \begin{equation} P(t) := \int \limits_0^1 p(x,t) \, \mathrm{d}x, \quad t \geq 0, \end{equation} is constant over time (i. e. $P(t) = P(0)$, $\forall \, t \geq 0$), ...

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System of quadratic algebraic equations
1 votes

This is a generalization of the scalar case $f(x) = a x^2 + b x + c = 0$. The derivative $f'(x) = 2 a x + b$ may be zero at a solution, which happens if and only if $b^2 = 4 a c$ (in which case the ...

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Writing a Matlab function after calling the ode45 solver
0 votes

You want to solve the initial value problem \begin{equation} \dot{x} = f(t,x), \quad x(0) = x_0, \end{equation} and then to evaluate the function $F : x_0 \mapsto y = x(T)$, where $T > 0$ denotes ...

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