Multistride L-Stable fourth-order methods for the numerical solution of ODEs

Recently, Chawla et al. [1] have obtained a one-parameter family of double-stride L-stable methods of fourth order by the coupling of three Linear Multistep Methods (LMMs). Here we present an alternative derivation technique based on mono-implicit Runge-Kutta (MIRK) methods. The MIRK method provides a framework within which all families of double- and triple-stride L-stable methods of fourth order can be expressed. The well-established theory for Runge-Kutta methods can then be used to derive these families in a straightforward manner.