We provide a new analytical approach to operator splitting for equations of the type u t = Au + uu x where A is a linear differential operator such that the equation is well-posed. Particular examples ...

The study of differential operators within the framework of Lie groups offers a profound gateway into understanding symmetry, geometry and representation theory. At its core, this area investigates ...

Mathematics of Computation, Vol. 59, No. 200 (Oct., 1992), pp. 403-420 (18 pages) We apply Runge-Kutta methods to linear partial differential equations of the form u t (x, t) = L (x, ∂)u(x, t) + f(x, ...

Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...

Introduces the theory and applications of dynamical systems through solutions to differential equations.Covers existence and uniqueness theory, local stability properties, qualitative analysis, global ...

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 ...