A partial differential equation (PDE) is a mathematical equation that involves multiple independent variables, an unknown function that is dependent on those variables, and partial derivatives of the ...

Continuation of APPM 5470. Advanced study of the properties and solutions of elliptic, parabolic, and hyperbolic partial differential equations. Topics include the study of Sobolev spaces and ...

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 ...

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 ...

SIAM Journal on Applied Mathematics, Vol. 43, No. 6 (Dec., 1983), pp. 1259-1273 (15 pages) A constructive algorithm is developed to determine whether or not a given linear p.d.e. can be mapped into a ...

Mathematical approaches for numerically solving partial differential equations. The focus will be (a) iterative solution methods for linear and non-linear equations, (b) spatial discretization and ...

In this article we study a class of stochastic functional differential equations driven by Levy processes (in particular, α-stable processes), and obtain the existence and uniqueness of Markov ...