Numerical methods with equation-dependent coefficients for stiff differential problems

The aim of this talk is to show techniques that allow to modify the coefficients of classic explicit numerical methods, improving their accuracy and stability properties, for the solution of ordinary differential equations systems of the following form: y′=f(t,y(t)) (3). The new methods coefficients depend on the Jacobian of the problem (3). In detail, we analyze the application of the mentioned methodologies on explicit Runge-Kutta methods and peer methods, proving that it is possible to make them A-stable, while preserving their explicit structure on several problems. We perform numerical tests to highlight the advantages of the new methods thus obtained, also showing the implementation details of the used Matlab codes.