SIAM Journal on Numerical Analysis, Vol. 51, No. 1 (2013), pp. 423-444 (22 pages) The theory of viscosity solutions has been effective for representing and approximating weak solutions to fully ...

In this paper we investigate the effectiveness of alternating direction implicit (ADI) time-discretization schemes in the numerical solution of the three-dimensional Heston-Hull-White partial ...

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 ...

Proceedings of the National Academy of Sciences of the United States of America PNAS is the world's most-cited multidisciplinary scientific serial. It publishes high-impact research reports, ...

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 ...

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 ...

Introductory course on using a range of finite-difference methods to solve initial-value and initial-boundary-value problems involving partial differential equations. The course covers theoretical ...