THIRD DERIVATIVE MONO-IMPLICIT RUNGE-KUTTA METHODS FOR STIFF ODEs

This work focuses on a Third-Derivative Mono-Implicit Runge–Kutta (TD-MIRK) method developed for the numerical approximation of stiff initial value problems (IVPs) in ordinary differential equations. The order conditions for the scheme are derived using Taylor series expansions. We introduce a seventh-order TD-MIRK method constructed to require the least possible number of function evaluations. The numerical experiments are then compared with well-known methods previously reported in the literature.