Numerical Stability Study of the Explicit-Implicit Range-Kuta Synthesis Methods (IMEX-ARK)

In this research we studied the numerical stability for Implicit-Explicit Additive Runge-Kutta (IMEX-ARK) methods which have the A[]-stability .This stability is equivalent A-stability of (B()-ARK) methods where B()=B1+(1-)B2 of second and third order for different intervals of values.This methods are suitable for solving stiff non-linear differential equations which has the form :

which contains stiff and non-stiff terms. We have used Matlab as programming tool .