How do you solve ordinary differential equations using two stage semi implicit inverse runge kutta schemes?

Answer 1

To solve ordinary differential equations (ODEs) using two-stage semi-implicit inverse Runge-Kutta schemes, you first discretize the time variable into small steps. In each time step, you compute intermediate stages that incorporate both explicit and implicit evaluations of the ODE, allowing for the treatment of stiff terms. Specifically, the scheme involves solving a system of equations derived from the implicit stages to update the solution at each time step. This method provides better stability properties for stiff problems compared to explicit methods.