- Miniker 102 manual
- - 1 An overview of the TEF formalism

## 1.2 Linearization and discretization in the TEF

The relations between sub-systems is excessively difficult to exhibit when having to cope with non-linear system. In the TEF, the TLS (Tangent Linear System) is constructed along the trajectory. One considers the system over a small portion along the trajectory, say between t and t + δt. The variation δη of η and δφ of φ is obtained through a Padé approximation of the state-transition matrix. The final form of the algebraic system is closed to the classical Crank-Nicolson scheme:

The blocks appearing in the Jacobian matrix are constructed with partial derivative of f and g, and with δt. From this system the elimination of δη leads to another formulation giving the coupling between transfers, and allows for the δφ computation. The δφ value is then substitued in δη to complete the time-step solving process.