Explicit peer methods with Jacobian-dependent coefficients

In this talk, explicit, parallelizable and optimally zero-stable peer methods with accuracy order p = s (s is the number of stages) are considered, and the application of a technique that leads to new coefficients dependent on the jacobian of the ordinary differential equations system to solve is shown. In fact, in this way, A-stable peer methods of order two and A(θ)-stable peer methods of order three preserving their explicit structure can be obtained. The analogies between the technique applied by us, TASE (Time–Accurate and highly–Stable Explicit) methodology [1] and non-standard finite differences [2] are discussed, and numerical tests confirming the derived theoretical properties of the analyzed peer methods are shown.