"FTCS" redirects here. For the scientific conference, see International Conference on Dependable Systems and Networks.
In numerical analysis, the FTCS (forward time-centered space) method is a finite difference method used for numerically solving the heat equation and similar parabolic partial differential equations.[1] It is a first-order method in time, explicit in time, and is conditionally stable when applied to the heat equation. When used as a method for advection equations, or more generally hyperbolic partial differential equations, it is unstable unless artificial viscosity is included. The abbreviation FTCS was first used by Patrick Roache.[2][3]
^John C. Tannehill; Dale A. Anderson; Richard H. Pletcher (1997). Computational Fluid Mechanics and Heat Transfer (2nd ed.). Taylor & Francis. ISBN 1-56032-046-X.
^Patrick J. Roache (1972). Computational Fluid Dynamics (1st ed.). Hermosa. ISBN 0-913478-05-9.
^Patrick J. Roache (1998). Computational Fluid Dynamics (2nd ed.). Hermosa. ISBN 0-913478-09-1.
artificial viscosity is included. The abbreviation FTCS was first used by Patrick Roache. The FTCS method is based on the forward Euler method in time...
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Finite volume method FTCSscheme Gilbreath's conjecture Sheffer sequence Summation by parts Time scale calculus Upwind differencing scheme for convection Paul...
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difference for the space derivative at position x j {\displaystyle x_{j}} (FTCS) gives the recurrence equation: u j n + 1 − u j n k = u j + 1 n − 2 u j n...
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