LAUSR

This paper develops and analyzes a new numerical scheme for solving hyperbolic conservation laws that combines the Lax Wendroff method with $$l_1$$l1 regularization. While prior investigations constructed similar algorithms, the method developed here adds a new critical conservation constraint. We demonstrate that the resulting method is equivalent to the well known lasso problem, guaranteeing both existence and uniqueness of the numerical solution. We further prove consistency, convergence, and conservation of our scheme, and also show that it is TVD and satisfies the weak entropy condition for conservation laws. Numerical solutions to Burgers’ and Euler’s equation validate our analytical results.