Differential equations are fundamental tools in physics: they are used to describe phenomena ranging from fluid dynamics to general relativity. But when these equations become stiff (i.e. they involve ...

SIAM Journal on Numerical Analysis, Vol. 27, No. 3 (Jun., 1990), pp. 704-735 (32 pages) Ordinary differential equations can be recast into a nonlinear canonical form called an S-system. Evidence for ...

Shock formation represents the process whereby smooth solutions to the governing equations of fluid dynamics undergo a transition to discontinuous states. In compressible fluid dynamics, this ...

In this paper we give a necessary and sufficient condition for the oscillation of the first-order neutral differential equations of Euler form with variable unbounded delays $\tfrac{d} {{dt}}\left( {x ...