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

Energy stable numerical methods for hyperbolic partial differential equations using overlapping domain decomposition

Article history: Received 15 April 2011 Received in revised form 16 February 2012 Accepted 13 March 2012 Available online 3 April 2012

Hyperbolic Partial Differential Equations

Evolution equations associated with irreversible physical processes like diffusion and heat conduction lead to parabolic partial differential equations. When the equation is a model for a reversible physical process like propagation of acoustic or electromagnetic waves, then the evolution equation is generally hyperbolic. The mathematical models usually begin with a conservation statement that ...

Numerical Methods for Partial Differential Equations

Partial Differential Equations with Numerical Methods

Robust Numerical Methods for Partial Differential Equations

The general theme of this project is to study numerical methods for systems of partial diffential equations which depend on one or more critical parameters. Typically, we are interested in systems which change type as a critical perturbation parameter tend to zero. Our goal is to construct numerical methods with convergence properties which are uniform with respect to the perturbation parameter...

Adaptive Collocation Methods for the Solution of Partial Differential Equations

An integration algorithm that conjugates a Method of Lines (MOL) strategy based on finite differences space discretizations, with a collocation strategy based on increasing level dyadic grids is presented. It reveals potential either as a grid generation procedure and a Partial Differential Equation (PDE) integration scheme. It copes satisfactorily with a example characterized by a steep travel...