  The standard methodology handling nonlinear PDE's involves the two steps:
numerical discretization to get a set of nonlinear algebraic equations, and
then the application of the Newton iterative linearization or its variants to
solve the nonlinear algebraic systems. Here we present an alternative strategy
called direct linearization method (DLM). The DLM discretization algebraic
equations of nonlinear PDE's is simply linear rather than nonlinear. The basic
idea behind the DLM is that we see a nonlinear term as a new independent
systematic variable and transfer a nonlinear PDE into a linear PDE with more
than one independent variable. It is stressed that the DLM strategy can be
applied combining any existing numerical discretization techniques. The
resulting linear discretization equations can be either over-posed or
well-posed. In particular, we also discuss how to create proper radial basis
functions in conjunction with the DLM.
