Stability of Numerical Schemes for PDE's
نویسنده
چکیده
The purpose of these notes is to give some examples illustrating how naive numerical approximations to PDE's may not work at all as expected. In addition, the following two important notions are introduced: (I) von Neumann stability analysis | helps identify when (and if) numerical schemes behave properly. (II) Arti cial viscosity | a tool in stabilizing numerical schemes. These notes should be read in conjunction with the use of the MatLab scripts (in the Athena 18311-Toolkit at MIT) whose names end with the acronym GBNS (for Good-Bad-Numerical-Schemes).
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