NESSi  v1.0.2 The NonEquilibrium Systems Simulation Library

## ◆ poly_differentiation()

template<typename T = double>
 T integration::Integrator< T >::poly_differentiation ( int i, int l )
inline

Returns the the weight needed for polynomial differentiation.

Purpose

Assuming the function $$f(x)$$ is given through points $$\{(x_l,f(x_l),l=0,\dots,k)\}$$\ with $$x_{l+1}-x_{l}=h$$, polynomial differentiation is defined by

\begin{align*} \frac{d}{dx}f(x)\big|_{x_i} = \frac{1}{h}\sum^k_{l=0} c_{i,l}\, f(x_l) \end{align*}

poly_differentiation returns the coefficient $$c_{i,l}$$ for given indicies $$i,l$$.

Parameters
 i First index of coefficients. l Second index of coefficients.

Definition at line 290 of file integration.hpp.

290 {return poly_differentiation_[i*(k_+1)+l];}