Accurate numerical discretizations of non-conservative hyperbolic systems

Accurate Numerical Discretizations of Non-conservative Hyperbolic Systems

We present an alternative framework for designing efficient numerical schemes for nonconservative hyperbolic systems. This approach is based on the design of entropy conservative discretizations and suitable numerical diffusion operators that mimic the effect of underlying viscous mechanisms. This approach is illustrated by considering two model non-conservative systems: Lagrangian gas dynamics...

On the Riemann Problem for Non-conservative Hyperbolic Systems

Hyperbolic Trajectories of Time Discretizations

A new paradigm for numerically approximating trajectories of an ODE is espoused. We ask for a one to one correspondence between trajectories of an ODE and its discrete approximation. The results enable one, in principal, to compute a trajectory of a discrete approximation, and to use this computation to rigorously prove the existence of a trajectory of the ODE near the discrete trajectory. More...

Numerical methods for hyperbolic systems

Numerical studies of non-local hyperbolic partial differential equations using collocation methods

The non-local hyperbolic partial differential equations have many applications in sciences and engineering. A collocation finite element approach based on exponential cubic B-spline and quintic B-spline are presented for the numerical solution of the wave equation subject to nonlocal boundary condition. Von Neumann stability analysis is used to analyze the proposed methods. The efficiency, accu...