STABLE COMPUTATIONS BY DISCRETE MOLLIFICATION

The discrete mollification method is a data smoothing procedure that is appropiate for the stabilization of explicit schemes for the numerical solution of partial differential equations and the regularization of ill-posed problems. This text introduces some of the main results and recent developments in discrete mollification and discusses several important topics on current research interest. The book develops and applies numerical methods based on discrete mollification for a variety of situations arising in applied mathematics, including convection-diffusion equations, conservation laws, strongly degenerate parabolic equations and several system identification problems.