Error bounds for the solution to the algebraic equations in Runge-Kutta methods (Q762892)

In the implementation of implicit Runge-Kutta methods the author considers the errors which are introduced due to the solution of the implicit equations. These errors can contaminate the final results. It is shown that these errors can be bounded independently of the stiffness of the differential equation considered if a certain condition is satisfied. This condition is also sufficient for the existence and uniqueness of a solution to the algebraic equations. From this point of view known methods are analyzed. An extension of known results is also given.