An advanced course in the analytical and numerical study of ordinary and partial differential equations, building on techniques developed in Differential Equations I. Ordinary differential equations: ...

Calculation: A representation of a network of electromagnetic waveguides (left) being used to solve Dirichlet boundary value problems. The coloured diagrams at right represent the normalized ...

Boundary value problems (BVPs) and partial differential equations (PDEs) are critical components of modern applied mathematics, underpinning the theoretical and practical analyses of complex systems.

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, ...

Partial differential equations (PDEs) are a class of mathematical problems that represent the interplay of multiple variables, and therefore have predictive power when it comes to complex physical ...

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 ...

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 ...

The members of the group Geometric Analysis and Partial Differential Equations have broad interests in analysis and geometry. Active research topics include quasiconformal analysis and partial ...

This paper extends the recent work on path-dependent PDEs to elliptic equations with Dirichlet boundary conditions. We propose a notion of viscosity solution in the same spirit as [Ann. Probab. 44 ...