4,427
edits
Continuous Time Random Walk: Difference between revisions
→The Master Equation
| Line 36: | Line 36: | ||
:<math>K( \Delta x, \Delta t; x,t) = p(\Delta x; x,t+\Delta t) \phi(\Delta t; x)</math> | :<math>K( \Delta x, \Delta t; x,t) = p(\Delta x; x,t+\Delta t) \phi(\Delta t; x)</math> | ||
While the Master Equation provides a very general description of transport, it does not allow a straightforward treatment of boundary conditions as with standard differential equations (except in special cases | |||
<ref>B.Ph. van Milligen, I. Calvo, and R. Sánchez, ''Continuous time random walks in finite domains and general boundary conditions: some formal considerations'', J. Phys. A: Math. Theor. '''41''' (2008) 215004</ref>). Thus, the final (quasi) steady state of the system is a function of the balance between sources and sinks. | |||
== Fractional Differential Equations == | == Fractional Differential Equations == | ||