Beam And Warming Scheme
In numerical mathematics, Beam and Warming scheme or Beam–Warming implicit scheme introduced in 1978 by Richard M. Beam and R. F. Warming, is a second order accurate Explicit and implicit methods, implicit scheme, mainly used for solving non-linear hyperbolic equations. It is not used much nowadays. Introduction This scheme is a spatially factored, non iterative, Alternating direction implicit method, ADI scheme and uses Backward Euler method, implicit Euler to perform the time Integration. The algorithm is in delta-form, linearized through implementation of a Taylor series, Taylor-series. Hence observed as increments of the conserved variables. In this an efficient factored algorithm is obtained by evaluating the spatial cross derivatives explicitly. This allows for direct derivation of scheme and efficient solution using this computational algorithm. The efficiency is because although it is three-time-level scheme, but requires only two time levels of data storage. This resul ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  

Explicit And Implicit Methods
Explicit and implicit methods are approaches used in numerical analysis for obtaining numerical approximations to the solutions of time-dependent ordinary and partial differential equations, as is required in computer simulations of physical processes. ''Explicit methods'' calculate the state of a system at a later time from the state of the system at the current time, while ''implicit methods'' find a solution by solving an equation involving both the current state of the system and the later one. Mathematically, if Y(t) is the current system state and Y(t+\Delta t) is the state at the later time (\Delta t is a small time step), then, for an explicit method : Y(t+\Delta t) = F(Y(t))\, while for an implicit method one solves an equation : G\Big(Y(t), Y(t+\Delta t)\Big)=0 \qquad (1)\, to find Y(t+\Delta t). Computation Implicit methods require an extra computation (solving the above equation), and they can be much harder to implement. Implicit methods are used because many pro ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]