Recent Progress in Studies of Stability of Numerical Schemes

Abstract

Applications and modeling of various phenomena in all areas of scientific research require finding numerical solutions for differential, partial differential, integral, or integro-differential equations. In addition to proving theoretical convergence and giving error estimates, stability of numerical methods for such operator equations is a fundamental property that it is necessary for the method to produce a valid solution. This Special Issue focuses on new theoretical and numerical studies concerning the techniques used for proving stability or instability of numerical schemes, which extend or improve known results. It also includes applications to non-linear physical, chemical, and engineering systems, arising in dynamics of waves, diffusion, or transport problems.