  Semi-implicit spectral deferred correction (SDC) methods provide a systematic
approach to construct time integration methods of arbitrarily high order for
nonlinear evolution equations including conservation laws. They converge
towards $A$- or even $L$-stable collocation methods, but are often not
sufficiently robust themselves. In this paper, a family of SDC methods inspired
by an implicit formulation of the Lax-Wendroff method is developed. Compared to
fully implicit approaches, the methods have the advantage that they only
require the solution of positive definite or semi-definite linear systems.
Numerical evidence suggests that the proposed semi-implicit SDC methods with
Radau points are $L$-stable up to order 11 and require very little diffusion
for orders 13 and 15. The excellent stability and accuracy of these methods is
confirmed by numerical experiments with 1D conservation problems, including the
convection-diffusion, Burgers, Euler and Navier-Stokes equations.
