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 ...

Pseudodifferential operators serve as a pivotal extension of classical differential operators by incorporating non-local features through their symbols. These operators are fundamental in the analysis ...

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 ...

We consider superlinearly convergent analogues of Newton methods for nondifferentiable operator equations in function spaces. The superlinear convergence analysis of semismooth methods for ...