  In this paper, a new implicit-explicit local method with an arbitrary order
is produced for stiff initial value problems. Here, a general method for
one-step time integrations has been created, considering a direction free
approach for integrations leading to a numerical method with parameter-based
stability preservation. Adaptive procedures depending on the problem types for
the current method are explained with the help of local error estimates to
minimize the computational cost. Priority error analysis of the current method
is made, and order conditions are presented in terms of direction parameters.
Stability analysis of the method is performed for both scalar equations and
systems of differential equations. The currently produced parameter-based
method has been proven to provide A-stability, for 0.5<\theta<1, in various
orders. The present method has been shown to be a very good option for
addressing a wide range of initial value problems through numerical
experiments. It can be seen as a significant contribution that the
Susceptible-Exposed-Infected-Recovered equation system parameterized for the
COVID-19 pandemic has been integrated with the present method and stability
properties of the method have been tested on this stiff model and significant
results are produced. Some challenging stiff behaviours represented by the
nonlinear Duffing equation, Robertson chemical system, and van der Pol equation
have also been integrated, and the results revealed that the current algorithm
produces much more reliable results than numerical techniques in the
literature.
