On the iterative solution of the algebraic equations in fully implicit Runge--Kutta methods
The paper is concerned with the iterative solution of stage equations given by a fully implicit Runge-Kutta method applied to stiff ordinary differential equations. The single-Newton iterative schemes defined here require only one LU-factorization per step and so the methods are preferable to other iterative schemes. The behavior of the iteration errors, independent of the stiffness, for single-Newton schemes and also for Newton-type iterations in general Runge-Kutta methods, is discussed. Finally, the results of some numerical experiments which confirm the theory are presented.
scientific article; zbMATH DE number 1456936