W-methods for semilinear parabolic equations Original Research Article

We study the temporal convergence behaviour of W-methods applied to semilinear parabolic equations. The stability and convergence analysis uses the framework of analytic semigroups of linear operators and perturbation techniques of such operators. The convergence order in general is a small non-integer, depending on the operator and the boundary conditions. Under additional conditions on the W-method the convergence rate can be increased.