the transport of dissolved contaminants in groundwater is usually described by the advectiondispersion equation with reaction. several numerical methods for solving the one-dimensional are availableincluding finite difference methods, finite volume methods, and finite element methods. stringent conditions,such as small peclet (pe) and courant (cr) numbers, must be satisfied to ensure the accura...

asphaltenes are the n-pentane or n-heptane insoluble fractions of crude oil that remain in solution under reservoir temperature and pressure conditions. they are destabilized and start to precipitate when the pressure, temperature and/or composition changes occur during primary production. the precipitated asphaltene particles will then grow in size and may start to deposit onto the production ...

We study the numerical approximation of viscosity solutions for Parabolic Integro-Differential Equations (PIDE). Similar models arise in option pricing, to generalize the Black–Scholes equation, when the processes which generate the underlying stock returns may contain both a continuous part and jumps. Due to the non-local nature of the integral term, unconditionally stable implicit difference ...

The emergence of self-organized behavior is characteristic of multi-particle systems in which individual motion is governed by the application of simple rules of interaction. The resulting dynamic order cannot be understood in terms of individual particles, but can be elucidated by formulating the system in terms of an abstract notion of dimensional coupling. We define this notion and consider ...