Numerical conservative solutions of the Hunter–Saxton equation
Katrin Grunert, Anders Nordli, Susanne Solem
Abstract
Abstract In the article a convergent numerical method for conservative solutions of the Hunter–Saxton equation is derived. The method is based on piecewise linear projections, followed by evolution along characteristics where the time step is chosen in order to prevent wave breaking. Convergence is obtained when the time step is proportional to the square root of the spatial step size, which is a milder restriction than the common CFL condition for conservation laws.
Topics & Concepts
MathematicsPiecewiseConvergence (economics)Conservation lawApplied mathematicsNumerical analysisSquare rootPiecewise linear functionMathematical analysisGeometryEconomicsEconomic growthNonlinear Waves and SolitonsNonlinear Photonic SystemsFractional Differential Equations Solutions