Finite Difference Methods
web.mit.edu › course › 16• develop upwind schemes for hyperbolic equations Relevant self-assessment exercises:4 - 6 49 Finite Difference Methods Consider the one-dimensional convection-diffusion equation, ∂U ∂t +u ∂U ∂x −µ ∂2U ∂x2 =0. (101) Approximating the spatial derivative using the central difference operators gives the following approximation at node i, dUi dt
Finite Difference Methods for Hyperbolic Equations | SpringerLink
link.springer.com › chapter › 10Abstract. Solution of hyperbolic equations is perhaps the area in which finite difference methods have most successfully continued to play an important role. This is particularly true for nonlinear conservation laws, which, however, are beyond the scope of this elementary presentation. Here we begin in Sect. 12.1 with the pure initial-value problem for a first order scalar equation in one space variable and study stability and error estimates for the basic upwind scheme, the Friedrichs ...