Stable computations by discrete mollification (2004)
The discrete mollification method is a data smoothing procedure, based on convolution, that is appropriate 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 of 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. For each topic there are theoretical considerations concerning stability and convergence and a generous amount of illustrative examples. The intended audience for this book includes mathematicians, physicists and engineers.