  In many applications, the governing PDE to be solved numerically contains a
stiff component. When this component is linear, an implicit time stepping
method that is unencumbered by stability restrictions is often preferred. On
the other hand, if the stiff component is nonlinear, the complexity and cost
per step of using an implicit method is heightened, and explicit methods may be
preferred for their simplicity and ease of implementation. In this article, we
analyze new and existing linearly stabilized schemes for the purpose of
integrating stiff nonlinear PDEs in time. These schemes compute the nonlinear
term explicitly and, at the cost of solving a linear system with a matrix that
is fixed throughout, are unconditionally stable, thus combining the advantages
of explicit and implicit methods. Applications are presented to illustrate the
use of these methods.
