Lax–Wendroff theorem
Encyclopedia
In computational mathematics
, the Lax–Wendroff theorem, named after Peter Lax
and Burton Wendroff
, states that if a conservative
numerical scheme
for a hyperbolic system
of conservation law
s converges, then it converges towards a weak solution
.
Computational mathematics
Computational mathematics involves mathematical research in areas of science where computing plays a central and essential role, emphasizing algorithms, numerical methods, and symbolic methods. Computation in the research is prominent. Computational mathematics emerged as a distinct part of applied...
, the Lax–Wendroff theorem, named after Peter Lax
Peter Lax
Peter David Lax is a mathematician working in the areas of pure and applied mathematics. He has made important contributions to integrable systems, fluid dynamics and shock waves, solitonic physics, hyperbolic conservation laws, and mathematical and scientific computing, among other fields...
and Burton Wendroff
Burton Wendroff
Burton Wendroff is an American applied mathematician and an Adjunct Professor at the Department of Mathematics and Statistics, University of New Mexico. He is also a retired Fellow and Associate at the Los Alamos National Laboratory...
, states that if a conservative
Conservation law
In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves....
numerical scheme
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
for a hyperbolic system
Hyperbolic partial differential equation
In mathematics, a hyperbolic partial differential equation of order n is a partial differential equation that, roughly speaking, has a well-posed initial value problem for the first n−1 derivatives. More precisely, the Cauchy problem can be locally solved for arbitrary initial data along...
of conservation law
Conservation law
In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves....
s converges, then it converges towards a weak solution
Weak solution
In mathematics, a weak solution to an ordinary or partial differential equation is a function for which the derivatives may not all exist but which is nonetheless deemed to satisfy the equation in some precisely defined sense. There are many different definitions of weak solution, appropriate for...
.