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6.3 NonLinear equations with CIP
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CFL limit 
Diffusion 
Lagrangian 
Nonlinear 
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The same approach is applicable more generally for nonlinear and vector
equations

(1) 
where
and
.
The problem is again decomposed in alternating phases with / without
advection describing the evolution of the function

(2) 
and by differentiation of (eq.6.3#eq.1), the evolution of the derivative

(3) 
Starting with the nonadvection phase, the discretized function is
first evolved according to

(4) 
where the superscript (
) refers to an intermediate step. To avoid an
explicit evaluation of
, the equation for the derivative
is computed with
The advection phase can then be evolved in the same manner as before
(eq.6.2#eq.4), by shifting the cubicHermite polynomials along
the characteristics (exercise 6.04).
SYLLABUS Previous: 6.2 CubicInterpolated Propagation (CIP)
Up: 6 LAGRANGIAN METHOD
Next: 6.4 Quiz
