Existence and Uniqueness of IRK Solutions
Since the Runge-Kutta methods studied in the foregoing sections are all implicit, we have to ensure that the numerical solutions, for which we have derived so many nice results, also really exist. The existence theory for implicit Runge-Kutta methods, presented in Volume I (Theorem 11.7.2), is for the non-stiff case only, where hL is small (L the Lipschitz constant). This is not a reasonable assumption for the stiff case.
Unable to display preview. Download preview PDF.