Lax-Wendroff's theorem
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 .
sentence
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:
- be consistent: for everyone is .
- be Lipschitz continuous in every argument.
- 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.
literature
- Randall J. LeVeque : Numerical methods for conservation laws. Birkhäuser, 1992, ISBN 978-3-7643-2723-1 .