Matrix-free \(W\)-methods using a multiple Arnoldi iteration (Q1902082)

A system of stiff differential equations \(y'= f(t, y)\), \(y(0)= y_0\in \mathbb{R}^n\) is studied by the use of \(W\)-methods. The Arnoldi iteration method and some of its extensions are used in case that several \(W\)- methods must be solved with the same matrix but with different right-hand sides, one after another. The methods are tested on three parabolic problems.