Lax-Wendroff's theorem

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The set of Lax-Wendroff states that if the numerical solutions of a hyperbolic conservation equation converge it with a weak solution converge the equation. It is a statement from numerical mathematics that is named after Peter Lax and Burton Wendroff .


Given a hyperbolic conservation equation with an initial value :

where is the function sought and the exact flow function . The numerical flow function is given. The following must also apply:

  1. be consistent: for everyone is .
  2. be Lipschitz continuous in every argument.
  3. the numerical approximations have compact support and limited variation : .

If the numerical approximations now converge:


so is a weak solution to the initial value problem.