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added van der pol oscillator example

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Krishna Vedala 2020-06-10 14:31:36 -04:00
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commit 2caed65a9c
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1 changed files with 22 additions and 8 deletions
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numerical_methods/ode_semi_implicit_euler.c
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@ -6,7 +6,7 @@
* [semi implicit Euler
* method](https://en.wikipedia.org/wiki/Semi-implicit_Euler_method)
*
* \description
* \details
* The ODE being solved is:
* \f{eqnarray*}{
* \dot{u} &=& v\\
@ -22,7 +22,20 @@
* The computation results are stored to a text file `semi_implicit_euler.csv`
* and the exact soltuion results in `exact.csv` for comparison. <img
* src="https://raw.githubusercontent.com/kvedala/C/docs/images/numerical_methods/ode_semi_implicit_euler.svg"
* alt="Implementation solution"/>
* alt="Implementation solution" width="350"/>
*
* To implement [Van der Pol
* oscillator](https://en.wikipedia.org/wiki/Van_der_Pol_oscillator), change the
* ::problem function to:
* ```cpp
* const double mu = 2.0;
* dy[0] = y[1];
* dy[1] = mu * (1.f - y[0] * y[0]) * y[1] - y[0];
* ```
* <a href="https://en.wikipedia.org/wiki/Van_der_Pol_oscillator"><img
* src="https://raw.githubusercontent.com/kvedala/C/docs/images/numerical_methods/van_der_pol_implicit_euler.svg"
* alt="Van der Pol Oscillator solution"/></a>
*
* \see ode_forward_euler.c, ode_midpoint_euler.c
*/
@ -44,9 +57,12 @@
*/
void problem(const double *x, double *y, double *dy)
{
const double omega = 1.F; // some const for the problem
dy[0] = y[1]; // x dot
dy[1] = -omega * omega * y[0]; // y dot
// const double omega = 1.F; // some const for the problem
// dy[0] = y[1]; // x dot
// dy[1] = -omega * omega * y[0]; // y dot
const double mu = 2.0;
dy[0] = y[1];
dy[1] = mu * (1.f - y[0] * y[0]) * y[1] - y[0];
}
/**
@ -62,10 +78,8 @@ void exact_solution(const double *x, double *y)
}
/**
* @brief Compute next step approximation using the midpoint-Euler
* @brief Compute next step approximation using the semi-implicit-Euler
* method.
* @f[y_{n+1} = y_n + dx\, f\left(x_n+\frac{1}{2}dx,
* y_n + \frac{1}{2}dx\,f\left(x_n,y_n\right)\right)@f]
* @param[in] dx step size
* @param[in,out] x take @f$x_n@f$ and compute @f$x_{n+1}@f$
* @param[in,out] y take @f$y_n@f$ and compute @f$y_{n+1}@f$