### Jacobian matrices

Stiff ODE solvers often execute faster if the Jacobian matrix, i.e. the matrix of partial derivatives of the RHS that defines the differential equations, is provided. The Jacobian matrix pertains only to those solvers for stiff problems (`ode15s, ode23s, ode23t, ode23tb`), for which it can be critical for reliability and efficiency. If the user does not provide a code to calculate the Jacobian matrix, these solvers approximate it numerically using finite differences. Supplying an analytical Jacobian matrix often increases the speed and reliability of the solution for stiff problems. If the Jacobian matrix is provided (symbolically) in the odefile, MATCONT stores as property the function handle of the Jacobian, otherwise this handle is set empty.

The standard MATLAB `odeget` and `odeset` only support Jacobian matrices of the RHS w.r.t. the state variables. However, we do need derivatives with respect to the parameters for the continuation. To compute normal form coefficients, it is also useful to have higher-order symbolic derivatives. To overcome this problem, MATCONT contains new versions of `odeget` and `odeset`, which support Jacobian matrices with respect to parameters and higher-order partial derivatives w.r.t state variables. The new routines are compatible with the ones provided by MATLAB.