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previously. For example, the simple forward Euler integration method would give, Un+1 −Un ∆t =AUn +b. (104) Using central difference operators for the spatial derivatives and forward Euler integration gives the method widely known as a Forward Time-Central Space (FTCS) approximation. Since this is an explicit method A does not need to

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~ ~ ~ ~~ ~ ~ ~ ~ ~ Series in Computational and Physical Processes in Mechanics and Thermal Sciences W. J. Minkowycz and E. M. Sparrow, Editors Anderson, Tannehill, and Pletcher, Computational Fluid Mechanics and Heat Transfer Aziz and Nu, Perturbation Methods in Heat Transfer Baker, Finite Element Computational Fluid Mechanics Beck, Cole, Haji-Shiekh, and Litkouhi, Heat Conduction Using Green ...

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The MacCormack method with flux correction requires a smaller time step than the MacCormack method alone, and the implicit Galerkin method is stable for all values of Co and r shown in Figure 8.1 (as well as even larger values). Each of these methods is trying to avoid oscillations which would disappear if the mesh were fine enough.

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The stability of MacCormack's method for the scalar advection equations. Appl. Math. Lett.4, 89–91 (1991). Article MathSciNet Google Scholar ...

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§ 7. High-order methods (construction of high-resolution TVD methods) 7.1 Artificial viscosity Example 1: Lax-Wendroff for u t +au x =0 with Artificial viscosity; Theorem 1: Linear monotonicity preserving methods have at most consistency order 1; Corollary 1: Stability concepts from Chapter 6.2 are equivalent for linear methods