Finite Difference Computing with PDEs by Hans Petter Langtangen & Svein Linge

Author:Hans Petter Langtangen & Svein Linge
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

we should get convergence rates r = 1 and p = 2 (C t and C x are unknown constants). As previously, in Sect. 2.​2.​3, we simplify matters by introducing a single discretization parameter h:

where K is any constant. This allows us to factor out only one discretization parameter h from the formula:

The computed rate r should approach 1 with increasing resolution.

It is tempting, for simplicity, to choose K = 1, which gives , expected to be . However, we have to control the stability requirement: , which means

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