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 ...

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 ...

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 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 ...

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 ...

THE main work of mathematical physicists is to represent the sequence of phenomena in time and space by means of differential equations, and to solve these equations. Even the revolution effected by ...

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, ...

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 ...